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14. Nuclei

(Nucleus - The Store House of Energy)

      The universe consists of MATTER and ENERGY. All the time matter is converted into energy. But for this phenomenon 'Life' would not have survived. This study of matter and energy is physics.
      Matter comprises of atoms. Matter can be converted into energy. Infact, Albert Einstein propounded that matter is a different form of energy! - Matter is a coiled energy!
      Tiny 'Atom' consists of a central nucleus around which electrons are revolving in circular orbits. The energy of an atom is stored in the nucleus - which is called 'Atomic energy' or 'Nuclear energy'. When lord Krishna while explaining the secrets (Science) of MATTER and Energy to Arjuna had shown his 'Viswa Roopa' (Cosmic form) which was as bright as thousnad Suns! When the first atom bomb was  exploded on the cities of Hiroshima and Nagasaki (Japan cities), the light emitted was more than that of 'Viswa Roopa'. That is what the author 'Robert Jugnk' describes in his famous book 'Brighter than Thousand Suns'. That is the power of nuclear energy, the energy in the nucleus. This chapter is the 'biography' of that Nucleus!
    Lord Rutherford discovered the central portion of an atom called "NUCLEUS" in which nearly all the mass of the atom was concentrated as a positive charge.

COMPOSITON OF THE NUCLEUS:
    Rutherford's experiment on the scattering of α particles, when they passed through a thin gold foil, showed that some α particles were deflected through more than 90º. From this experiment Rutherford concluded that in every atom there exists a small entity where all the positive charge is crowded, which exerts a strong force of repulsion on the α particles. This small entity, carrying a positive charge is called 'NUCLEUS'.
     The nucleus is spherical in shape and has a radius of 10−15 m. Now the question is what are the constituents of nucleus.
    The entire mass of atom is concentrated inside the nucleus. The nucleus consists of positively charged protons and chargeless neutrons. Proton has a positive charge equal in magnitude to that of the charge of an electron. The mass of proton is greater than that of electron. The neutron is chargeless whose mass is little more than that of proton.
Protons and Neutrons are the constituents of nucleus and are called 'NUCLEONS'.
     The total number of nucleons in the nucleus of an atom is called the 'mass number' and is denoted as 'A'.

      The number of protons in an atom (nucleus) is called the atomic number and is denoted as 'Z' and the number of neutrons is denoted as 'N'.
                                              Thus A = Z + N
     It is a convention to write the nucleus of an atom as  where 'X' represents the chemical symbol of the element whose atomic and mass numbers are 'Z' and 'A' respectively.
     For example, 92U235 represents that U is a symbol of Uranium whose atomic number is 92 and mass number is 235. Similarly, for Helium 2He4 (Atomic number 2 and mass number 4).
       Thus 92U235 represents the Uranium nucleus which contain 235 nucleons (92 protons and 143 neutrons).


NUCLEUS SIZE - TIP OF A PIN IN AN AUDITORIUM
       The size of a nucleus in an atom can be compared to the tip of a pin kept at the centre of a circular auditorium. That way the whole of the atom is filled almost with empty space.
Rutherford's experiments of α (alpha) particle scattering established the size of the nucleus. i.e., the radius of the nucleus is found to be approximately equal to 10−15 m.
 The 'volume' of the nucleus (V) is found to be proportional to its 'mass number'.

     Considering the nucleus is spherical in shape of radius 'R' and mass number 'A', its volume can be written as
               V

 A


    
 Nuclear distances are measured in units called 'Fermi'.
      1 Fermi (F) = 10−15 m
 'Fermi' is named after scientist Enrico Fermi, whose theories on nuclear fission are well known.
Electron Volt (eV) - Unit of atomic energy
      For measuring energies in atomic reactions 'Joule' (J) is not a convenient unit as it is very large. Electron Volt (eV) and especially its size is convenient. For example, to remove one electron from an atom of Hydrogen 13.6 eV of energy required.
 An electron volt (eV) is the amount of energy that should be given to an electron of charge 1.6 × 10−19 coulombs (c) on being accelerated through a potential difference of one volt.
 ... 1 eV = 1.6 × 10−19 × 1 J = 1.6 × 10−19 J
     Nuclear forces are very much larger than atomic forces. Therefore in dealing with nuclei, bigger unit, a million electron volt (MeV) equal to 106 eV is used.

Units of masses of Electron, Proton and Neutron
      Although 'eV' used as the unit of atomic and nuclear energies, another unit of energy is that of mass, as mass and energy are mutually convertible according to the 'Theory of Relativity' of Albert Einstein and the famous equation E = mc2 (Matter is form of coiled energy).
    As the masses of atoms, nuclei and the fundamental particles (electron, proton, neutron etc) are very very small, and more over they are not visible for naked eye.
    Their masses cannot be find by using a balance as the masses of other objects are found in ordinary life!
    Hence in order to express the masses of elementary particles a new unit called atomic mass unit (amu or U) has been adopted.

    Thus 1 amu (U) =   (mass of Carbon)

Where N is Avogadro number i.e. number of atoms in 1 gm of Carbon
       = 6.02 × 1023 = 6.02 × 1026 kg mol−1

1 amu = 1.66 × 10−27 kg.
On this scale,
i) The mass of proton is 1.00752 U = 1.652 × 10−27 kg
ii) The mass of electron is 0.00055 U = 9 × 10−31 kg
iii) The mass of neutron is 1.00893 U = 1.674 × 10−27 kg
Applying Einstein's formula for mass - energy equivalence E = mc2, be find that when 1 amu of mass is annihilated, it is equivalent to energy given by
  E = 1.66 × 10−27 × (3 × 108)2 J


   
     = 931 × 106 eV
Thus 1 amu = 931 MeV
and 1 electron mass = 9 × 10−31 kg = 0.5 MeV

NUCLEAR FORCES
        It is quite amazing to note that the nucleons in a nucleus are together and remain intact in such a small size approximately 10−14 m. The question is that what is the type of these strong attractive forces which bind these nucleons together in nucleus?


                            

       These attractive forces cannot be the electrostatic coulomb forces between charged particles or gravitational forces. If electrostatic force is present, the repulsion between two protons (as they are positively charged) would make the nucleus most unstable. They cannot account for the strong forces between the nucleons which are responsible for the large binding energy in the nucleus which is the order of 1 MeV per nucleon. Even the gravitational force cannot account for the same, as the gravitational force between two nucleons is infinitesimally small. Therefore, to account for the existence of nuclei, a very 'strong force' called 'nuclear force' has to be considered.
 

FEATURES OF NUCLEAR FORCES
      The electrostatic coulomb forces act between any pair of charges at any distance are obeying inverse square law. But the situation in case of nucleons in a nucleus is different, as they are closely packed in a tiny nucleus. The forces which hold the nucleons together exists between the individual neighbouring nucleons separated by a distance of the order of 10−15 m. Thus the nuclear forces between the nucleons are 'short range forces'! Operating over very short distances.

THREE KINDS OF FORCES
  Nuclear forces are of three kinds.
     1. The force between a proton and a neutron (pn force)
     2. The force between two protons (pp force)
     3. The force between two neutrons (nn force)
     All these forces are 'attractive forces'. Incase of (pp) nuclear force there is also a repulsive force between two protons, but this is a weak force compared to the strong nuclear force there is an experimental evidence to show that (pp), (pn), (nn) forces are equal there by showing that the 'nuclear force is charge independent' i.e. it does not depend on the charge of the particle.
     'Yukawa' and 'Meson': On theoritical basis in 1935 Yukawa, a Japanese scientist predicted a new particle, the Meson which could have a positive or negative charge or may be a neutral. He assumed this new particle is exchanged between the nucleons and the corresponding exchanging force is responsible for the binding energy of the nucleons.
     Nuclear forces are thus produced by a 'Meson field' similar to the electromagnetic field but of shorter range. The prediction of Yukawa was confirmed by the experimental discovery of μ 'meson' in 1936 and π 'meson' in 1947.

     Anderson and Needer Mayer observed experimentally these particles in 1936 while investigating cosmic rays and gave the name. 'Mesotrans' (In Greek meaning intermediate, their mass being in between that of proton and electron). Later the abbreviated name 'Meson' was given by Homi J.Bhabha, the Indian scientist in the year 1939 which is now in popular usage.
 

ORDER OF MAGNITUDE OF FORCES BETWEEN NUCLEONS
    The order of the magnitude of strong attractive nuclear forces can be illustrated with the following example.
The distance 'r' between the electron and the proton in the hydrogen atom is about
5.3 × 10−11 m.
From Coulomb's law, the electrical force between them is

The gravitational force between them is given by

       Thus, the electrical force is about 1039 times stronger than the gravitational force(A piece of paper left from a height falls on the ground because of gravitational force.
This piece of paper can be easily attracted by a glass rod rubbed with silk possessing electrical force!!)
    Now, let us consider the repulsive coulomb force between two protons, in a nucleus of Iron separated by a distance of 4 × 10−15 m.

      To compensate this enormous repulsive force, the attractive nuclear forces between nucleons must be stronger i.e. greater in magnitude. This example shows that the nuclear binding forces are much stronger than atomic binding forces. Atomic binding forces are in turn, much stronger than gravitational forces.

The (pp), (pn) and (nn) nuclear forces are equal.
      The magnitude of the coulomb energy between two protons is nearly equal to 2.5 MeV. This energy is very small compared with the average binding energy per particle which is about 8 MeV.
Nuclear forces are strongest forces in nature.
The gravitational, electrical (Coulomb's) and nuclear forces between nucleons are in the ratio
   Fg : Fe : Fn = 1 : 1036 : 1038

 They depend on the spin of the nucleon. When the spins of two nucleons are parallel the forces between them are strong. If the spins are antiparallel, the forces between nucleons are weak.
 These forces will not act along the line joining the nucleons i.e. they are non central forces.
 Each nucleon attracts those nucleons which are just next to it. It will not attract all the nucleons. Thus nuclear forces are saturated forces.
 Nuclear forces are due to the result of the exchange of Π mesons between the nucleons. Thus they are exchange forces.

MASS DEFECT AND NUCLEAR BINDING ENERGY:
     In general, it has been found that mass of a nucleus is less than sum of the masses of protons and neutrons which constitute the nucleus.
    For example, consider the 2He4 nucleus. Helium nucleus has 2 neutrons and 2 protons and the mass of the Helium nucleus is 4.0016 U.
     Mass of 2 protons = 2 × 1.0075 = 2.0150 U
     Mass of 2 neutrons = 2 × 1.0089 = 2.0178 U
     Total mass = 4.0328 U
        Thus, the mass of constituent parts of helium nucleus is greater than the mass of the helium nucleus. In general, this is the case with all the nuclei.
       This difference between the real mass of a nucleus and the sum of the rest masses of its constituent nucleons is called the mass defect.
    For helium, mass defect = 4.0328 − 4.0016 = 0.0312 U

How to account for this mass defect?
BINDING ENERGY

      As the mass of a nucleus is found to be less than the sum of the masses of its protons and neutrons, the protons and neutrons are brought together to form the nucleus, there is a decrease in mass. According to Einsteen's mass - energy relation, the disappearence of mass Δm is accompanied by the release of an amount of energy E = Δm.c2 where c is the velocity of light in vacuum. This energy gives the necessary potential for the nucleons to bind together and is called the binding energy, which is due to the decrease in the total mass defect of the system i.e. mass defect is converted into binding energy correspondingly, the same energy must be given to the nucleus if it is required to break the nucleus into parts.
     Thus, binding energy is the energy liberated when 'Z' protons and 'N' neutrons combine to form a nucleus (or) it is the work required to separate a nucleus into its neutrons and protons.
    Binding energy Eb is given by
    Eb = [(mass of Z protons + mass of N neutrons) - mass of nucleus)]
          = Δm . c2 where Δm is the mass defect

In general, binding energy per nucleon is calculated,

Where A is the total number of nucleons (neutrons and protons) in the nucleus. A graph is shown between binding energy per nucleon and mass number A 


         

The following facts found experimentally about nuclear binding energy.
1. Greater the binding energy per nucleon, the more stable is the nucleus.
2. Binding energy rises sharply for low value of mass number A.
3. He4, Li8, C12 and O16 are more stable than other nuclei.
4. The maximum value of binding energy per nucleon is 8.8 MeV

 

DISCOVERY OF 'NEUTRON'
      According to Rutherford and Bohr atom models the mass of an atom is primarily due to the mass of the nucleus which contains positively charged particles called 'Protons'.
Then, Why Neutrons?
    It is found that 'atomic mass', in case of light nuclei, is approximately twice the mass of protons in them and in case of heavier nuclei this ratio is more. For example, the atomic mass of helium is 4.0026 U and its atomic number is 2 (Atomic number is number of protons in an atom). Similarly, this kind of anomaly was found in case of other elements. Inspite of different theories put forward, this discrepancy of the mass of the nucleus continued until Rurtherford had 'predicted' the existence of a particle along with proton inside the nucleus which is chargeless (neutral) called 'neutron' as early as 1920. Neutrons should be 'chargeless because in atom, the negative charge of the electrons are balancing the positive charge on the protons inside the nucleus and neutrons should account for the atomic mass of the atom along with the protons.

      But no experimental evidence of neutron was obtained as it was an uncharged particle; so it could not be detected by any particle detector like 'Wilson Cloud Chamber'.
     In 1930, The German scientists 'Bothe' and 'Becker' reported that when certain light elements, like Beryllium and Boron, were exposed to α particle radiation from Polonium, a very highly penetrating radiation was obtained, which they thought might be high energy gamma rays.
    Joliot - Curies (Frederic Joliot, husband of Irene Curie, daughter of Marie (Madam) Curie - both husband and wife are Noble laureates for their discovery of 'artificial radioactivity' - 'Nobel' has become a family affair!!) investigated that these radiations knock out protons from paraffin and other substances containing hydrogen.
The process can be represented as shown in figure 2.

    But Joliot - Curies were not aware of Rutherford's prediction ten years earlier, and they were not able to give any explanation of this radiation.
    The experiment was repeated by James Chadwick, a British scientist in 1932 who gave a satisfactory explanation by suggesting that the unknown radiation consisted of uncharged particles of mass similar to that of protons. These particles are called 'Neutrons'.
The neutrons are emitted according to the equation.
1) In case of Beryllium
      4Be9 + 2He4 6C13  6C12 + 0n1 (neutron)
2) In case of Boron
       5B11 + 2He4 7N14 + 0n1 (neutron)
As neutron is chargeless, it has high penetrating power.
Neutron is represented by 0n1 because it has zero charge and its mass number is unity.

A schematic diagram of Chadwick's apparatus is shown in figure 3. 


    
'S' is a source of alpha particles (Polonium) and 'T' is a Beryllium target placed in a chamber 'C' which is highly evacuated. α particles from the source 'S' hit the target 'T' and the resulting particles are registered in a cloud chamber (ionisation chamber D) with a window 'W'. A Paraffin slab can be placed between 'C' and 'D' when desired. Chadwick observed that when Paraffin was not placed, very few counts were registered in the counter. But when a thin slab of Paraffin was placed infront of D, the number of counts increased. This is because of the fact that neutrons in collision with the hydrogen atoms contained in Paraffin give up their energy to the protons of hydrogen atoms, and these protons emitted from Paraffin are recorded. But, if the Paraffin slab is removed, the number of counts again reduces considerably. This is due to the fact that neutrons being uncharged, they by themselves cannot produced ionisation directly in the chamber. Even the few counts registered before introducing the Paraffin slab are due to the ions ejected by neutrons from the walls of the chamber.

Properties of Neutron
     1) Neutron is one of the fundamental particles forming the nucleus of elements and the charge on it is zero.
     2) As it is uncharged particle, it is not deflected by electric and magnetic fields.
     3) They do not produce ionisation in gases, being charge less.
     4) They are highly penetrating.
     5) As they are electrical neutral, they disintegrate nuclei of other atoms effectively.
        7N14 + 0n1 4C14 + 1H1 (Proton)
       6C14 + 0n1 7N14 + −1e1 (β - particle)
     6) Slow neutrons are very effective in bringing nuclear fission.
     7) A free neutron is unstable particle and undergoes radioactive beta decay into a proton, an electron and a neutrino.


     
The half − life for this decay is 1.3 minutes.

Uses of Neutron
    1) Neutrons are used in research work in Physics, Chemistry, Medicine and Biology.
    2) Slow neutrons are used in nuclear fission in atom bomb.
    3) Fast neutrons are used in disintegration of nuclei to get radio-isotopes which have great importance in medicine, biology, agriculture and industry etc.
Radioactivity - Prelude to Nuclear Fission
    It is an astonishing phenomenon exhibited by nature. While studying the fluorescent effects of cathode rays, Roentgen (the first Noble Prize winner in Physics in 1901) a German Physicist made a startling discovery in 1895 that when fast moving cathode rays strike an obstacle, an unknown, invisible, penetrating radiation originates from the point, where the cathode ray particles are brought to rest and called them X - rays. (It is the style of mathematics to assume any unknown quantity as 'X'). 
    On hearing Roentgen's work, the French Physicist Henry Becquerel wanted to investigate if there was any connection between X - rays and the light emitted by a fluorescent material. He found that a crystal of Potassium uranyl sulphate, when exposed to sunlight, emitted radiation which was able to pass through a black paper and effect a photographic plate placed under it.

     At first he thought the effect was caused by sunlight, inducing fluorescence. But on one occasion in 1896, it so happened that it was cloudy for three days and he could not expose the crystal to sunlight and kept in darkness of a table drawer, over photographic plates wrapped in a black paper. As the sun has refused to shine on the fourth day, he developed the photographic plates 'just for interest' expecting certain faint images on them. But he was surprised to find that the images were very well developed. This showed that the sunlight was not the cause of the penetrating radiation as was originally supposed. In fact it was shown that this potassium uranyl sulphate was emitting an invisible and penetrating radiation. Whether it was exposed to sunlight or shut in darkness. On further investigation, it was found that radiation were able to pass through opaque materials and also cause ionisation in air. These rays were called 'Becquerel rays'.
Marie Curie enters on the stage
    At the end of 1895, Marie Curie, a brilliant young and remarkable Polish scientist, was looking for a new field of research for her doctoral thesis. She found 'Becquerel rays' was suitable subject about which very little was known at that time.

      She was constantly aided by her guide and professor Piere Curie, who subsequently became her husband. The first result which madam Curie obtained in her research was that the intensity of radiation given off from a particular sample of Potassium uranyl sulphate was proportional to the quantity of 'uranium' present in it. This led her to believe that the 'radiation' was an 'atomic property'. She set out to examine the compounds of all elements to see if they also produce radiations of this type. Soon she found that 'Thorium' also emitted such radiations. Thus, no more these radiations were the property of radium only and so they could not be labelled as 'uranium rays'. In 1898, she suggested the name 'Radioactivity' for the phenomenon (from Latin word 'radius' for a ray).
    Next, she directed her attention in examining all minerals containing uranium and thorium. She found that the intensity of radioactivity shown by mineral Pitchblende (the ore of uranium) is much greater than that yielded by similar quantities of uranium in pure state. Hence it was evident to Curies that there was another element of great radioactive strength present in the mineral, Pitchblende. After a very elaborate and tedious process of chemical treatment and fractional crystallisation, they isolated from Uranium ore another concentrated radioactive element called 'Polonium' (named after Marie Curie's native country Poland).

But the intensity of radioactivity from Pitchblende was so great that both Uranium and Polonium contents could not account for. After a few months Curies isolated from tons of Pitchblende ore decigram (a very small quantity) of new element called 'Radium' and found that it emitted radiations much stronger (a few million times) than Uranium (the name radium for the intense radiations associated with it). All these radioactive radiations which can pass through all substances could not penetrate through lead.
      Marie Curie had the rare distinction of being the only scientist to be awarded Nobel Prize twice in two basic branches of science, namely Physics along with Piere Curie and Becquerel and later after the death of her husband in chemistry all byherself. But the most tragic thing is, Madam Curie became victim of her, own invention. The radiations of 'radium' which cure the deadly disease like cancer, had entered her body and affected all the vital organs (which was not known in those days) and killed her. A candle while give 'light' to the surroundings melts by itself.

     Experiments by Becquerel and Curies in France, Rurtherford in England, showed that there were three types of radioactive radiations which, in increasing order of penetrating power were called, alpha (α), beta (β) and gamma (γ) rays (radioactive decay).
    This phenomenon was named as 'radioactivity' and exhibited by the elements whose atomic numbers range from 83 to 92.
   Thus, radioactivity is the spontaneous disintegration of nuclei of atoms of high atomic weight with emission of certain penetrating radiations.
    The radioactive radiations are due to the disintegration of the nucleus of an atom and positively charged α - particles should not be misunderstood with protons, negatively charged β particles with electrons in the orbit and neutral γ rays with neutrons of an atom. All these radiations are emenating from nucleus.
    Thus breaking of nucleus in 'radioactivity' can be considered as a prelude of breaking of the nucleus by scientists in future by 'nuclear fission'.
 'Radioactivity can be considered as a phenomenon in which unstable nucleus under goes a decay which is called 'radioactive decay'.

Three types of radioactive decay occur in nature.
   i) α - decay in which a helium nucleus 2He4 is emitted.
  ii) β - decay in which electrons or positrons (particles having same mass has that of electrons, but with a charge opposite to that of electrons i.e. of positive charge)
  (iii) γ – decay in which high energy (hundreds of keV) photons are emitted.
Alpha decay
Example: Decay of 'Uranium' to 'Thorium' with emission of helium nucleus.
       92U238   90Th234 + 2He4
     In α - decay, the mass number of the product nucleus is four less than the decaying nucleus while the atomic number decrease by two.
    The decaying nucleus is called 'parent nucleus' while the product nucleus is called 'daughter nucleus' (probably, because Mary Curie had two daughters and not a son!!)
     In general, α decay of a parent nucleus.
   ZAX results in a daughter nucleus Z−2YA-4
  ZAX Z−2YA−4 + 2He4

     From Einstein's mass - energy equivalence E = mc2, and principle of conservation of energy, it can be seen that this spontaneous decay is possible only when the total mass of the decay products is less than the mass of the initial nucleus. This difference in mass appears as kinetic energy of the products.
       The disintegration energy or the Q - value of nuclear reaction is the difference between the initial mass - energy and the total mass - energy of the decay products.
    For α decay, Q = (mx − my − mHe) C2
Q is also the net kinetic energy gained in the process or, if the initial nucleus X is at rest, the kinetic energy of the products. Clearly, Q > 0 for exothermic processes such as α - decay.
Beta - decay
     In beta decay, a nucleus spontaneously emits a negatively charged beta particle (β− decay) or a positron (β+ decay).
    A common example of β− decay is 


  
and that of β+ is
   11Na22 10Ne22 + e+ + ν

      In β− decay the emission of negatively charged β particle is accompanied by emission of anti nutrino (β−).
    In β+ decay, a neutrino (ν) and positron are emitted.
 Neutrino is neutral particle with no charge, and almost zero mass. (Neutrino meaning little neutral one) and hence it cannot interact with matter. So its detection is very difficult. It can penetrate large quantity of matter even earth without any interaction.
     Neutrinos are generated on a large scale in the sun in nuclear reactions.
    In radioactive decay it was found that the laws of conservation of momentum and energy were obeyed in case of α and γ decay, but not in β decay. To account for this discrepancy, Wolfgang Pauli postulated the existence of this new particle 'neutrino'.
    In both β− decay and β+ decay, the mass number A remains unchanged. In β− decay, the atomic number 'Z' of the nucleus goes up by 1, while in β+ decay 'Z' goes down by 1. The basic nuclear process underlying β− decay is the conversion of neutron to proton.


    
While for β+ decay, it is the conversion of proton into neutron.
     p  n + e+ + ν
    While a free neutron decays to proton, the decay of proton to neutron is possible only inside the nucleus, since proton has smaller mass than neutron.

Gamma Decay
     Just like in an atom, a nucleus also will have discrete energy levels i.e. the ground state and excited states. But the scale of energy is very different. Atomic energy level spacings are of the order of eV, where as the difference in nuclear energy levels is of the order of MeV. When a nucleus in an excited state spontaneously decays to its lower energy state, a photon is emitted with energy equal to the difference in the two energy levels of the nucleus. This is called gamma decay. The energy (in MeV) corresponds to radiation of extremely short wavelength, shorter than the hard X - rays.
Laws of Radioactive Decay
     According to Soddy and Rutherford, radioactive atoms are unstable and they disintegrate (decay) according to the laws of probability (laws of chance). The disintegration of a single atom is accompanied by α or β particle or X - ray. The disintegration occurs at random from a radioactive substance as regards with time and direction which particular atom of the substance disintegrates first depends upon chance only. Radioactivity is a statistical phenomenon.

Laws of Decay
     1st Law: Every atom of radioactive element is constantly breaking into fresh radioactive products with emission of alpha, beta and gamma rays. The new products have entirely new chemical and radioactive properties than that of the parent atom.
     2nd Law: The rate of disintegration i.e. the number of atoms breaking per second at any instant, is directly proportional to the number of atoms present (just as in our daily life, normally not a miser, the rate at which we spend our money depends on the money that present in our Wallet!!) at that instant and is independent of the external physical conditions like temperature, pressure (atmospheric conditons), chemical conditions etc.
     Suppose at a time 't' there are 'N' radioactive atoms in an element.
     Let 'dN' atoms disintegrate in a time 'dt'. As the rate of disintegration is directly proportional to the number of atoms present.


   
    Where 'λ' is called 'the radioactive constant on decay (disintegration) constant.

    The negative sign shows that with increase in disintegration, the value of N decreases (as money decreases with spending).


  

Where k is constant of integration.
When t = 0, N = N0 where N0 is the number of atoms originally present.
log N0 = k
Substituting this value of k in equation (i)
log eN = − λt + logeN0

 or N = N0e λt

   This shows that the number of radioactive atoms in a radioactive element decreases exponentially with time.
This is known as disintegration law of radioactive element.
The graph between 'N' and 't' is shown in figure 4.
Half - life period (T)
    The half-life period of a radioactive substance is defined as the time required for one half of the original radioactive atoms of the substance to disintegrate.
    Why half life period? for all the atoms of a radioactive element to disintegrate it takes millions of years which is called Life Period of that element. Hence half life period is considered and defined. So, half life period is not half of life period, but time taken for half the atoms to disintegrate.
    Let T be the half - life period of a radioactive substance.
    We know N = N0e λt   (ii)
    If N0 is the original number of atoms.
    After a time t = T (half life period), the number of atoms present = 


Thus, half - life period depends upon the disintegration constant (λ) of the substance and is different for different substances.
     In figure 4, half life period of radioactive substance is shown. It should be remembered that after twice the half - life period, about one quarter of the substance still remains. The whole substance will take a very long time to disintegrate completely, as shown by 'exponential curve' running parallel to the time axis.

    To understand what is half - life let us consider 'radium' as illustration. One half of any number of radium atoms will disintegrate into simpler atoms in 1620 years.
    One half of what remains on one fourth of original atoms will decay in next 1620 years and so on. This period of 1620 years is called half-life of radium.
Nuclear Fission - Principle of 'ATOM BOMB'!
    In 1934, Enrico Fermi and his co-workers attempted to form the elements beyond Uranium (Z = 92) which at that time was the last element in periodic table. As they knew, by that time, that the emission of a 'β particle' increases the atomic number by one. They bombarded uranium with neutrons, which emitted β -particles with different half-periods. Thus trans - uranic elements whose atomic numbers is greater than 92 were discovered.
     In 1938, Otto Hahn and Strassmann made similar experiments and were investigating the effects of 'bombarding Uranium' with 'slow neutrons'. By careful chemical analysis of the products, they found that one of the product nuclei was an isotope of 'Barium' of atomic number 56 (56Ba141) and not a heavier element, as predicted by Fermi. They further found that 'Barium' was accompanied by a radioactive element of the gas 'Krypton' (Z = 36). The atomic numbers of these two nuclides add upto 92 i.e. atomic number of Uranium.

    It remained for Madam Meitner and her nephew Frisch in January 1939 to take lead in these investigations. Referring to Hahn and Strassmann's experiments, they stated that ''It seems possible that Uranium nucleus has only small stability of farm, and after neutron capture, it divides itself into two nuclei of roughly equal size".
    The name 'fission' was given to this process, as it resembled division of cells in biology (from the Latin word 'fizzion' which means 'cleaving'). Further they found that only Uranium - 235 undergoes this process of fission, though naturally occuring Uranium has 93.3% of Uranium - 238 and 0.7% of Uranium - 235. It is of historical interest to note that this discovery was made in Germany a few months before the beginning of the Second World War.
Thus, Nuclear fission is the process of breaking up of the nucleus of a heavy atom into two, more or less equal fragments, with the release of large amount of energy.
When Uranium - 235 is bombarded with neutrons, a Uranium nucleus captures a slow neutron, forming an unstable compound necleus (92U236). The compound nucleus splits into two nearly equal fragments, Barium (56Ba141) and Krypton (36Kr92), releasing 3 neutrons and energy Q. (figure 5)


       The reaction can be written as
      92U235 + 0n1 56Ba141 + 36Kr92 + 3 0n1 + Q
Energy released in Fission
      In the process of nuclear fission, a large amount of energy is released. The energy is produced, because the original mass of the nucleus of Uranium, before fission is greater than the sum of the masses of the products after fission. The difference between the masses, before and after fission, is converted into energy according to Einstein's equation E = mc2.

     The energy liberated per fission is calculated by considering the fission reaction as follows:
     92U235 + 0n1 56Ba141 + 36Kr92 + 3 0n1 + Q (energy)

  This decrease in mass is converted into energy.
          Since 1 amu = 931 MeV

  ... Energy released = 0.2253 × 931 = 209.8 MeV
   Thus, in the process of fission of one nucleus of Uranium, about 200 MeV energy is released.
     It is found that 1 kg of Uranium after fission delivers as much energy as the combustion of about 3000 tonnes of coal. This energy is known as nuclear or atomic energy.
Level of Nuclear Energy
     The nuclear energy of about 200 MeV is accounted for as the sum of the energy of γ rays (6 MeV), the kinetic energy of the fission fragments (168 MeV), energy of emitted neutrons (6 MeV) and radioactive decay energy (21 MeV). The energies of the fission fragments, neutrons and gamma rays are almost immediately converted into 'heat energy', where as the decay energy of the fission products, which are radioactive is converted into heat over the period during which the decay takes place. The fission of U - 235 nucleus can, therefore, be thought of as causing immediate release of 180 MeV of energy in the form of heat. This correspond to a continuous power production of about 1000 kilo watts which is sufficient ten thousand 100 W burning by a system consuming by fission no more than 1 gm of Uranium per day.
     Thus, here was a source of power, whose potentialities were far superior than those of fuels such as coal and oil.

Note: Fission is not similar to radioactivity in heavy elements because in that only a very small portion of the nucleus goes of at a time. Where as in fission the nucleus splits up into fragments of comparable size.

Theory of fission - Liquid drop model:
    Bohr and Wheeler successfully explained the phenomenon of nuclear fission on liquid drop model. They considered the nucleus to be a drop of liquid. The shape of the nucleus is spherical and acted upon by
        i) The surface tension force and
        ii) Coulomb repulsive force

    When a neutron is captured by a nucleus i.e. nucleus is bombarded by a neutron, oscillations are setup within the drop (nucleus) which tend to distort the spherical shape, so that the drop becomes ellipsoid in shape (fig 6). If the energy of the neutrons is very large, the drop may acquire the shape of dump bell. Each bell of the dump bell has now a positive charge. The coulomb repulsive force may then push the two fragments apart and fission takes place.
Uses of nuclear energy:
    1. It is used in the production large amount of electricity. It is the cheapest and clearest form (no pollution) of energy.
    2. Nuclear explosive is used in mining and petroleum recovery.
    3. In the production of radioisotopes which are useful in curing diseases like cancer.
    4. Used for production in agriculture and as a fuel in running big factories, trains and cars.
Chain Reaction
    A chain reaction is a self propagating process, in which number of neutrons multiply rapidly during fission, till the whole of the fissible material is disintegrated (figure 7).

      

       When one U235 atom undergoes fission, it releases three neutrons. If more than one of these neutrons is able to cause fission in the other U235 nuclei, the number of neutrons increase rapidly. Thus a 'chain reaction' of breaking up nuclei is produced, which once started, goes on till the entire U235 is disintegrated, releasing a large amount of energy. Due to the fission 250 gm of Uranium, the energy produced is equivalent to five million kilowatt hours. This is due to only one neutron and this process takes only about 10-6 of a second. If this process is allowed to continue without any control, enormous amount of energy is released which causes a violent explosion and destroys everything that is on its way. This is (the principle of) atom bomb. Atom bomb is 'the uncontrolled chain reaction'. If the amount of Uranium is too small, the chain reaction can stop before it releases energy required for explosion.
    Hence, if the chain reaction to start, it is necessary that the mass of Uranium be greater than certain minimum mass called 'critical mass' or 'critical size'.
Moderator: The fast moving neutons during fission can be slowed down by a material called 'Moderator' which is arranged among the Uranium rods. The moderators must not absorb neutrons. The function of the moderator is to slow down the neutrons to thermal neutrons. Heavy water, graphite, beryllium etc are used as moderators.

Controller: By use of materials like Cadmium, which absorbs neutrons without their participation in disintegration, the chian reaction can be controlled. Thus by properly controlling chain reaction, a constant level of power output can be maintained. Such a controlled 'chain reaction' will be a very efficient source of power. This is the process which takes place in an atomic reactor.
Thermal Neutrons: When fast moving neutrons are passed through paraffin moderator elastic collisions takes place between neutrons and hydrogen nuclei in paraffin. They exchange their velocities and neutrons are slowed down. These neutrons are called 'thermal neutrons' and are used in nuclear reactors.
Nuclear Reactor: A nuclear reactor is a device in which enormous amount of nuclear energy is produced by controlled chain reaction.
      Here a vast amount of energy is produced from a small amount of fuel. It is some times called atomic reactor or atomic pile.
    The first reactor was installed and operated by Ernico Fermi and his co-workers in Chicago in 1942.

    A nuclear reactor generates energy mainly in the form of heat by means of nuclear fission. An atomic bomb gets destructive power from uncontrolled fission, where as in nuclear reactor the fission is under control. Hence, the energy it produces can be produced for generation of electricity and for peaceful purposes. Reactors are also used to convert different elements into radioactive isotopes.
    Nuclear reactors differ in size and design. But most of them will have the following main features.
  1) The core 2) The Moderator 3) Control System 4) The neutron reflector 5) The coolant 6) Safety system (Sheilds)
1. The core: This is central part of the reactor, where "fissionable material' called 'Fuel' is kept and fission occurs. The commonly used fissionable materials are (a) natural Uranium containing 92.18% of U235 and 0.82% of U238 only one of these isotopes U235 actually undergoes fission (b) the Thorium isotope Th232 (c) Plutonium isotopes Pu239, Pu240 usually, the fuel is kept in different aluminium cans in form of cylindrical rods placed at some distance apart.

2. The moderator: It is a material used to increase the probability of fission and thus promote the chain reaction. The function of the moderator is to slow down the highly energetic neutrons released by U235 during fission which are again captured by fresh amount of U235 to split in turn. If moderator did not slow down the neutrons, many of them would be absorbed by U238 atoms, which do not undergo fission.
 Heavy water (a compound composed of Oxygen and Deuterium), Graphite, Beryllium etc are used as moderators.
3. Control system: The control system regulates the rate of chain reaction and prevents it from running spontaneously. This is achieved by pushing control rods into the reactor core. Those rods are made of Cadmium or Boron. These rods absorb the neutrons, without undergoing change and thus cut down the level of reactivity.
4. The neutron reflector: By the use of reflectors on the surface of the reactors, leakage of neutrons can be reduced very much and the neutron flux in the interior can be increased.
5. Coolant (Cooling system): The collant removes the heat produced by fission as soon as it is liberated in the reactor core. It makes the heat available to other systems of nuclear power plant for the generation of electricity etc. This is evolved from the kinetic energy of the fission fragments, when they are slowed down in the fissionable substance and by the moderator. Coolant also controls the temperature of the reactor core and prevents it from getting over-heated. Coolants used are a) air, CO2 (or) He b) water (or) other liquids c) certain metals (or) alloys.

6. Sheilds: To save the workers near the reactor from the harmful effect of various types of radiations like gamma rays. Emitted from the reactor, thick walls of cement, concrete and lead are constructed around the reactor which are called shields.
     For emergence shut downs tiny bells of Samarium oxide, a compound of Samarium and Oxygen are dropped into the core, which absorb enough neutrons to stop the chain reaction. This is called safety system.
Power Reactor
     The heat generated in a nuclear reactor is used to produced electric power in a nuclear power plant. The main features of a power plant are shown in figure 8.

     Certain quantity of Uranium in the form of pure metal or a solution, forms the source of heat energy (fuel). A large amount of heat is produced in the fission process. The Cadmium rods regulate the temperature to the desired value.
    If it is required to lower the temperature, the Cadmium rods are inserted deep down, so as to absorb more neutrons. If the temperature has to be increased, Cadmium rods are pulled out a little, to the requirement. A fluid, liquid sodium alloyed with Potassium (molten metal), is circulated through the shielded reactor and the heat energy of this molten metal is transferred to water in a heat exchanger, and the water in turn converts into steam. The steam that is generated operates a convential turbine to produce electricity.
Nuclear Holocaust
    On August 6, 1945 U.S. dropped an atom bomb on Hiroshima, Japan. The explosion was equivalent to 20,000 of tons of TNT. Instantly the radioactive products devasted 10 sq. km of the city which had 3,43,000 people, out of which 66,000 were killed and 69,000 were injured.
India - Atomic energy
    The atomic energy programme of India was launched under the guidance of Homi J.Bhabha.

Reactors of our country
         i) First nuclear reactor in India - APSARA (1956)
         ii) Cyrus (Canada - India research US) - 1960
         iii) Zerlina
         iv) Purnima (1, 2 and 3)
         v) Dhruva
         vi) Kamini
Nuclear Fusion - Principle behind Hydrogen Bomb! and also 'Sun shines'!!
 Nuclear fusion is the synthesis of lighter nuclei.
   In this process two or more light nuclei combine (fuse) together to form a single heavy nucleus.
    For example, when two deutrons (four hydrogen nuclei) fuse together, a helium nucleus is formed and in addition 24 MeV of energy is released. The mass of the single nucleus of helium formed is less than the sum of the masses of the individual light nuclei. The difference in mass is converted into large amount of energy, according to Einstein's mass-energy equation E = mc2.
1H2 + 1H2 2He4 + 24 MeV energy
 (Deutrons)         (Helium)

Energy released
       The initial mass of two Deuterium nuclei = 2 × 2.01364 = 4.02728 U
       Mass of Helium nucleus = 4.0016 U
       Decrease in mass = 4.02728 - 4.0016 = 0.02568 U
       But 1 amu (U) = 931 MeV
       Energy released in fusion = 0.02568 × 931 = 24 MeV
 The energy released in fusion i.e. 24 MeV is much less than the energy liberated in the fission of Uranium, which is about 200 MeV. But, energy released per unit mass during fusion of light nuclei is much greater than compared to the fission of Uranium; because, for a given mass the number of light nuclei are more where as the Uranium particles are less in number.
Conditions under which fusion occurs
     For the fusion process to take place, the light nuclei must have very high speeds in order to overcome the large coulomb repulsion at very small distances and these speeds must be maintained. To obtain these speeds, the material must be heated to extremely high temperatures of the order of 107 to 108 K (this is the temperature of the interior of the sun).

       Therefore, before fusion takes place, the light nuclei must have their temperature raised by several millions of degrees kelvin through fission process. At these temperatures the atoms are completely dissociated into bare nuclei and electrons (hence it is also called 'electron soup'). This results in fourth state of matter, a fully ionised form known as Plasma, which consists of nuclei of light elements such as deutrons, protons, tritons and also electrons moving rapidly in all directions. As no material wall can contain such a plasma at very high temperature, a type of magnetic bottle i.e. a suitably, designed magnetic field, can hold such matter. In such a process, plasma is compressed, and a very high temperature, suitable for nuclear fusion is produced. These types of reactions, in which violent thermal collisions are produced between the nuclei of the substance subjected to very high temperature, is called 'thermo nuclear reactions'.

     The high temperature needed to initiate the fusion process is produced by fission. (Is it that one should explode 'atom bomb', i.e. fission bomb in order to explode hydrogen bomb i.e. fusion bomb?!!). The latest device used for producing very high temperature suitable for fusion is by concentrating the 'Laser beam'.
Difference between fusion and fission
   Fusion cannot take place until the fusible material is ignited, where as any thermal neutron can start a chain reaction in fission.
The amount of fusible material in a fusion bomb (hydrogen bomb) is not limited, where as the material in a fission bomb (atom bomb) is limited to a certain mass; while the fission of a nucleus produces radioactive wastes like Barium and Krypton which are harmful, the products of fusion are almost harmless. The wastes of atom bomb cause harm for future generations. But hydrogen bomb is more powerful.
Energy of Sun and stars (even Sun is a star!)
Throughout the ages, man has viewed the Sun and the stars with awe and wonder. Their existence and the source of their energy (heat and light) has been explained by numerous theories.

     Scientists are not certain as to what processes have led to the formation of the universe, but they are agreed that the source of solar and stellar energy is nuclear and that the reactions involved are fusion type, which are likely to happen at very high temperatures (15 to 30 million kelvin) found in the interior of the stars.
     The Sun radiates 3.8 × 1026 J of energy per second. The temperature of the interior of the Sun is about 2 × 107 K and the temperature of some of the stars is of the order of 108 K. In 1938, C.Weizsaecker in Germany and Hans Bethe in U.S.A., both working independently, gave detailed theory of nuclear reactions in the Sun and the stars. The theory involves the synthesis of protons to give Helium. Carbon acts as a catalyst in the nuclear reactions.
     All the light elements like Hydrogen and Helium are in the state of plasma at such high temperatures and all the electrons are stripped of the atoms. The energy produced in fusion is responsible for the maintenance of the high temperature of the stars and also for the emission of energy by radiations.

    The Carbon - Nitrogen cycle is responsible for nuclear fusion of protons and enormous amount of energy is produced during the process. The cycle is represented by the following set of equations (reactions).
       6C12 + 1H1 7N13 + energy (γ rays) (1)
       7N13 6C13 + 1e0

 (2)
                                       (positron)
       6N13 1H1 + 7N14 + energy (γ rays)  (3)
       7N14 1H1 + 8O15 + energy  (4) 
       8O15 7N15 + 1e0   (5)
                                      (positron)
       7N15 + 1H1  6C12 + 2He4 (6)
    The reaction (1) is caused by the collission of a proton with a carbon nucleus, resulting in the formation of nitrogen - 13 and the release of energy (reaction 1).
   The nitrogen - 13 is isotope, radioactive and decays with the emission of a positron to carbon - 13 (reaction 2).

6C13 further captures a proton and more energy is released (reaction 3).
7N14 further captures a proton and energy is released (reaction 4)
8O15 is radioactive and gives out a positron (reaction 5).
7N15 further captures a proton and 6C12 is again produced (reaction 6).
   Thus, in the process, 4 protons combine to produce the Helium nucleus and enormous amount of energy is released. Carbon acts as a catalyst. The energy released in each fusion is approximately 25 MeV.
Adding above all six equations
      4 1H1

 2He4 + 2 1e0 + 2 υ
                                                      (Neutrinos)
      4 1H1 = 4.03100 amu; 2He4 = 4.002603
      2 1e0 = 0.001098 amu
      Loss in mass = 0.02756 amu.
      According to Einstein's mass - energy equivalence energy released = 0.02756 × 931 = 25.6 MeV.

     It is found that in one million years in the Sun loses about 10-7 of its mass by this process. Taking the mass of the Sun as 2 × 1030 kg and its present age as 1010 years, it is estimated that the carbon - nitrogen cycle may continue for another 30 billion years. So there is no danger for Sun or neither for us in near future!!
Proton - Proton Cycle
   In the Sun and other stars, where the temperature is less than 107 K, fusion takes place by 'proton - proton cycle' as follows:
     1H1 + 1H1 1H2 + 1e0 + υ (neutrino)   (i)
                                             (positron)
     1H1 + 1H2 2He3 + energy  (ii)
     2He3 + 2He3 2He4 + 1H1 (iii)
Multiplying (i) and (ii) by 2 and addding to (iii)
     1H1 + 1H1 + 1H1 + 1H1 2He4 + 2 1e0 + 2 υ + energy
The net result is same as that of carbon cycle.

      The proton - proton cycle is an important source of energy in the Sun and stars of low temperatures like Red - dwarfs. From this cycle it can be concluded that the older stars have more Helium than the younger ones. When 'Energy' coiled in the matter has been projected by phenomenon like 'Radioactivity', 'Nuclear fission' and 'Nuclear fusion', these great events have been explained by that mystical equation E = mc2, propounded by the brilliant science icon of 20th century, namely Albert Einstein.
Mass - Energy equivalence
    That the mass of a body is constant was accepted without question until Albert Einstein showed by means of his special theory of Relativity that the mass of the body was not independent of its velocity, but was given by the expression


    

     Where m0 is the mass of a body when it is at rest relative to the observer, and m is the mass when it is moving with a velocity ' v' relative to the observer, 'c' being the velocity of light.
      If 'ν' is very much smaller than 'c', 'm' is almost equal to m0, and this explains why no change in mass of bodies such as bullets, aeroplanes etc is detected when they are in motion. But as 'ν' approaches 'c' in value where c is the velocity of light in vacuum, the term  gets smaller and so 'm' increases.
      If the velocity of the object relative to the observer is same as that of light, then the value of 'm' would be infinite.
   If the above expression is expanded mathematically, it becomes


to the body when it is given the velocity v. Hence the body acquires, at the same time an increase in mass and proportionate increment in its kinetic energy.
    This led Einstein to suggest that the total energy of a body should be given as
E = mc2 = m0c2 +

 m0v2 (1)
      Therefore a body has energy m0c2, even when it is at rest and this if matter (i.e. mass) can be destroyed (annihilated) energy can be released.
     The truth of this statement was demonstrated to the world with the horrible explosion of atom bomb at Hiroshima in 1945. Thus no longer the conservation laws of matter and energy could be separated, as maintained by classical physics. But, in their place stands one universal law, which states that 'mass and energy are mutually convertible but their sum total remains constant in any reaction'. This is called mass - energy equivalence.

From equation (i),  m0v2 = (m − m0)c2
    Thus according to Einstein, kinetic energy is equal to the increase in mass (m − m0) multiplied by c2.
      In other words, mass is a form of energy or vice versa i.e. any form of energy must have a mass.
    From the expression E = mc2, if 1 gram (10−3 kg) of matter is annihilated, the energy produced = 10−3 (3 × 108)2 = 9 × 1013 J.
     No doubt, it is a surprising fact, but the disintegration of a piece of radium producing enormous energy by way of heat is a proof of this fact. It has been calculated that the amount of energy emitted during the transformation of 1 gm of radium is of the order of 2 × 1010 kilocalaries, which would be able to raise 2 × 108 kg of cold water to its boiling point.

Conclusion
Was Einstein a 'wicked' scientist?

     As atom and hydrogen bombs are basing on the principle of E = mc2, people misunderstood that because of Einstein, the devasting bombs were invented. But, the fact is Einstein revealed the mysterious energy possessed by the matter. How to make use of that energy to the benefit of humanity is left to the wisdom of humanity. After all, fire can be used to cook the food, as well as to burn a house!!
Books for further reading
     1. Brighter than Thousand Suns
     2. Children of Ashes (Robert Jugnk) (Penguin Ed's)
     3. Einstein's Cosmos by MICHIO KAKU
     4. Marie Curie: A Life by Susan Quinn

              Rome was not built in a single day, so the 'Nucleus' the heart of an atom. It is quite amazing that the nucleons (protons and neutrons) are together and remain intact in such a small size of 10-15 meters and possess enormous energy. The binding energy that forms nucleus is proportional to the number of nucleons. The nucleus is spherical in shape and has a radius of the order of 10-15m is called 'fermi' (F). The radius of an atom is nearly 10-10 m. If an atom were enlarged to the size of a bus, the nucleus would be like the dot at the end of this sentence.
              Lord Rutherford discovered the central portion of an atom called 'nucleus' in which the mass and the energy of an atom is concentrated. The discovery of the phenomenon of 'Radio Activity' by Henry Becquerel paved the way for a new branch of physics called 'Nuclear Physics'.
Thomson - Roentgen - Becquerel
              While studying the effects of cathode rays (electrons) discovered by J.J. Thomson in 1879, Roentgen made a startling discovery of X-rays, a penetrating, invisible radiation in 1895. On hearing Roentgen's work, the French physicist Henry Becquerel wanted to investigate if there was any connection between X-rays and light emitted by fluorescent material.

He found that certain crystals when exposed to sunlight emitted radiation which were able to pass through a black paper and affecting photographic plates. He thought the effect was caused by sunlight inducing fluroscence.
When Sun felt Shy to Shine....
              In 1896 it so happened that sky was cloudy for three consecutive days and Becquerel could not expose the crystal ' Potassium Uranyl Sulphate ' (Luckily for humanity, he laid his hand on this, mysterious crystal) to the sunlight with disgust thrown the crystal into the dark corner of his laboratory cup board. As the sun has refused to shine on the fourth day also, he wanted to relax for some time from his scientific work, in taking photographs of his girl friend!
Friends picture along with 'Lab Key':
              When Becquerel developed the photo film from his camera, he found to his surprise, along with his friend, his laboratory key was also photographed. But who on this work, photographs the key of a lab? He knew that the duplicate key of his lab was left in the cupboard along with the photographic film wrapped in black paper. He reasoned out that an unknown and mysterious radiation in the darkness of the cupboard was exposing the photographic film penetrating black paper in which it was wrapped.

The lab key which was there in the path of the radiation was photographed. When Becquerel searched in the cupboard for source of radiation he found with other things like paper clips, rubber bands, the 'Potassium Uranyl Sulphate' which he left in the cupboard.
Becquerel Rays
              Infact, it was shown that potassium uranyl sulphate crystal was emitting an invisible and penetrating radiation, even when it was shut in darkness without exposing it to sunlight. On further investigation, it was found that these radiations were able to pass through opaque materials and also cause ionisation in air. These rays were named as 'Becquerel Rays'.
Marie Curie - Two 'NOBELS':
              At the end of 1895, Marie Curie, a young beautiful, brilliant and remarkable polish lady was looking for new field of research for her doctoral thesis. She found Becquerel rays were a suitable subject. She was constantly helped by her guide Pierre Curie (who later became her husband and thus Curie was added to her name) and found that the intensity of radiation emitted from 'Potassium uranyl sulphate' was proportional to the quantity of 'Uranium' present in it. Soon she found that the element 'Thorium' also emitted such radiations. Directing her attention to 'pitch blend' (one of uranium) -

- Madam Curie isolated 'Polonium' (named after her native country) and radium (emitting more radiations) along with 'Uranium'. She named 'Radioactivity' for the Phenomena (from the latin word 'Radius' for ray). Marie Curie had the rare distinction of being the only scientist to be awarded the Nobel Prize twice in two basic branches of science, namely physics (along with Pierre Curie and Becquerel) and later in chemistry all by her self. But, it is a great tragedy that Marie Curie died of ' Lukemia' (Blood Cancer) which she acquired without her knowledge, because of constant exposure to the Radioactive radiations.
Radioactivity:
               Radioactivity is the spontaneous disintegration of nuclei of atoms of high atomic weight with emission of penetrating radiations called α, β and γ rays which are in increasing order of penetrating power.
               The radioactive radiations are due to the disintegration of the nucleus of an atom and positively charged α − particles should not be misunderstood with 'Protons' (positive charge) negatively charged β − particles with 'Electrons' (negative charge) revolving in the orbits of an atom and chargeless γ − rays (waves) with the neutrons (chargeless) in an atom. All these radiations are emanating from the nucleus.          

        The ionising power of α - particles is 100 times greater than that of β − rays and 1000 times than that of γ − rays .Electromagnetic waves of very small wavelength of range of 1°A.
Laws of Radioactive displacement:
Law 1:
If an atom of radioactive element emits an α - particle of charge 2 and mass 4, its atomic number decreases by ' 2 ' and atomic weight by ' 4 ', and the atom (parent element) is transformed into another element (daughter element) of lower atomic number. The place of new atom goes down in ''Periodic table'' by two placed.


                            
  (atomic)Radium        emissions of          Radon
  (parent element)      α - particle          (Daughter element)
Law 2: When a radioactive element emits a β − Particle of charge ' 1 ' and of negligible mass, it is converted into a new element of atomic number ' 1 ' greater than that of parent element, but of same atomic weight as the parent element. Thus, the place of the new atom goes up in the 'Periodic table' by one place.

(Parent element)    Emission of β − particle    (Daughter element)

At the end: The new atom formed, may itself be 'Radioactive' and by disintegration of a new atom and so on. Thus, a chain of radioactive elements (radioactive series) is formed by successive, disintegration, until a stable element 'isotope of lead' is formed when radioactivity
ceases.
No sons only daughters: Since Curie couple don't have sons but only daughters 'Irene' and 'Ruth'. Probably they have called the element formed after disintegration they have called it a 'daughter element'.
Radioactive series are four in number:
                            i) Uranium-radium series 
                            ii) Actinium series
                            iii) Thorium series 
                            iv) Neptunium series

 Only α or β and not both - one at a time!!
               It has been formed that in a radioactive transformation, either an α − particle or a β − particle is emitted by an atom at a time. Both are not emitted simultaneously nor two particles of the same kind are emitted simultaneously by the same atom.
Laws of Radioactive decay or disintegration:
Matter of chance & Randomness:

               Radioactive atoms are unstable and they disintegrate according the 'Laws of chance' (Laws of probability). The disintegration of a single atom is accompanied by α or β − particle. The disintegration occurs at 'random' as regards both time and direction. Which particular atom of the substance disintegrates first depends upon chance only.
* 'Radioactive decay' is a statistical phenomenon-
1st law of decay: Every atom of 'Radioactive element' is constantly breaking into fresh radioactive products with emission of alpha, beta and gamma rays. The new products (daughter elements) have entirely new chemical and radioactive properties than that of the parent element.
2nd law of decay: The rate of disintegration i.e. the number of atoms breaking per second at any instant is directly proportional to the number of atoms present at the instant- 

- and is independent of the external physical conditions like temperature, pressure and chemical combination etc.
(It is some what like our spending the money at a time, depends on the amount of money in our pocket!)
* Suppose at a time '' t '' that there are '' N '' radioactive atoms in an element and
'' dN '' atoms disintegrate in a time dt, then according to 2nd law of decay,


                   
Where λ is called radioactive or decay (disintegration constant)
* The negative sign shows that with the increase in disintegration, the value of N decreases.
* If N0 is the number of atoms present originally in the element, it can be show that


                     
             This shows that the number of radioactive atoms in a radioactive element decreases 'exponentially' with time. i.e; as time lapses the process of decay slows down.
Half-life Period:
           As the elements of natural 'Radioactivity decays' very slowly i.e; -

the whole radioactive substance will take very long time to disintegrate completely, scientists consider a concept called 'Half life period'.
* The half life period of a radioactive substance is defined as the time required for one half of the original radioactive atoms of the substance to disintegrate.
* If T is the half life period of a radioactive substance, it can be shown that 
                                
Where ' λ ' is the disintegration (decay) constant of the substance.
* Thus, half life period depends upon the disintegration constant of the substance and is difficult for different substances.
* To understand what is half-life period, let us consider radium as illustration. One half of any number of radium atoms will disintegrate into simpler atoms in 1620 years. One half of what remains or one fourth of original atoms will decay in next 1620 years and so on. This period of 1620 years is called half-life of radium.
Artificial or induced Radioactive - Even light elements:
               Uranium and other radioactive elements, their nuclei being unstable, -

- disintegrate spontaneously emitting alpha, beta and gamma rays. This phenomenon is called ''Natural Radioactivity''.
               But, many of the stable i.e. non-radioactive chemical elements can be made radioactive artificially by irradiating them with 'neutrons' or bombarding them with heavy particles like protons, alpha particles etc.
               In 1934 'Irene Curie' (daughter of Curies) and her husband 'Joliot Curie' found that some light elements like Boron, Magnesium and Aluminium became radioactive when bombarded by alpha particles from Polonium. They emitted radiations even after the bombardment had ceased. This phenomenon of converting a stable atom into a radioactive atom by bombarding it with fast moving particles is called 'Artificial or induced Radioactivity'.
* The activity of these radioactive products decrease with time, as in case of, natural radioactivity, but their 'half life periods' are 'very short'.
               The particles emitted by artificial radioactive elements are usually 'Electrons' and 'Positrons'. Positrons, the antimatter of electron were discovered originally by Anderson while studying the action of cosmic rays in magnetic field.

Some nuclear reactions:
              'Radio Phosphorus' is produced by bombarding 'Aluminium' with alpha particles from Polonium.
                        13Al37            +    2He4         15P30      +    0n1
            (Aluminium)                 alpha                  Radio            neutron
                                                  particle            phosphorus
              That is aluminium is now transformed into Radio Phosphorus, which is an 'isotope' of phosphorus. If the atomic number remains the same, but the mass numbers are different, then the elements formed are called isotopes of a single element ' H ' .
              For example 1H1, 1H2, 1H3 i.e; a single hydrogen, heavy hydrogen (deutron) and tritium respectively, are isotopes of single element hydrogen. Similarly the radioactive phosphorus is an isotope of phosphorus and such isotopes are called 'radio isotopes'.
              This radioactive phosphorus, having a half-period of 2.5 minutes is most unstable disintegrates. Producing a stable atom of silicon with an emission of positron (1e0)
 1)       15P30         14Si30     +     1e0
                                     (Silicon)        (Positron)   

2)     6B10      +      2He4    

       7N13     +     0n1
           Boron                                      Radio isotope of nitrogen
             7N13         6C13     +     1e0
                                                       Positron
* The Half life period of 7N13 is 11 minutes.
* Artificial radioactivity has also been observed when elements are bombarded by protons. neutrons, deutrons and photons. The artificially radioactive elements (radio isotopes) emit only positrons or electrons, some times accompanied by γ − rays and do not emit α − particles like natural radioactive elements.
             Nowadays radio isotopes are prepared by placing stable elements inside nuclear reactors (In India at Bhabha Atomic Research Centre, Bombay) The large number of neutrons produced in the reactor are used to bombard the desired elements. The important radio isotopes so produced are Iodine-131, Phosphorus-30 and Cobalt-60

Half life of few Radioactive  elements and Isotopes

Application of Radio Isotopes:
i) In medicine:
for diagnosis and treatment of diseases.
* A lot in the blood stream can be diagnised and located
* Radio Sodium is used as a tracer element to study the progress of circulation of medicines in the body

* Leukemia disease is treated by radiation from radio isotopes of phosphorus
ii) In Biology: Radio isotopes are used in molecular biology for producing destructive effects.
* Radioactive radiators sterilize 'Pharmaceutical' and surgical instruments.
iii) In Agriculture: Radio Isotopes are used as tracer elements.
* By using radio- isotopes, new characteristics in plants can be created.
iv) In Industry: Radio isotopes are used in the study of mechanism of friction by fast moving machines and to measure the wear and tear.
* Radio-isotopes are used to detect flaws in metal castings, in controlling the thickness of paper, plastic and rubber sheets.
Radio Carbon dating (Carbon-14 Dating):
               It is a method of determining the age of objects like rocks, ancient manuscripts, upto 10,000 years old containing matter that was once living such as wood.
Discovery of ' Neutron ':
               Rutherford had predicted the existence of Neutron as early as 1920. But no experimental existence was obtained as it was an uncharged particle, so it could not be detected by any particle detector like cloud chamber.            

                In 1930, the German scientists Bethe and Becken reported that when certain light elements like 'Beryllium' and 'Boron' were exposed to alpha particle radiation from Polonium, a very highly penetrating radiation is obtained; which they thought might be high energy gamma rays.
               Joliot - Curie investigated that these radiations knockout protons from paraffin and other substances containing hydrogen.


  
  
 Joliot Curie were not aware of Rutherford's prediction 10 years earlier and they were not able to give any explanation of this radiation.
              

 The experiment was repeated by Chadwick in 1932 who gave a satisfactory explanation by suggesting that the unknown radiation consisted of 'uncharged particles' of 'mass similar to that of ' Proton'. These particles were called 'Neutrons'.
The neutrons are emitted according to the equation;
1) Incase of Beryllium:     4Be9 + 2He4   6C13      6C12 + 0n1
                                                                                                            (Neutron)
ii) Incase of Boron:           5B11  +  2He4       7N14   +   0n1
                                                                                               (Neutron)
Atomic Energy:
Nucleons: The nucleus consists of 'Proton's and 'neutrons' which are called 'nucleons'. Proton has a positive charge equal in magnitude to that of the charge of the electron (1.6 ×
10-19 coulombs). The mass of Proton is greater than that of electron. The neutron is chargless whose mass is little more than that of proton.
Nuclear forces: To account for the existence of nucleus, a very strong force called 'nuclear force' has to be considered. These are short range forces and operate only between two neighbouring nucleons and are of three kinds.

They are:
1) The force between a Proton and a Neutron (pn - force).
2) The force between two protons ( pp - force).
3) The Force between two neutrons (nn - force).
i) These are attractive forces of equal magnitude and are independent of charges.
ii) These are the strongest forces in nature. The gravitational,electrical (coulombs) and nuclear forces between the nucleons are in the ratio.
                                   Fg : Fe : Fn = 1 : 1036 : 1038
iii) They depend on the spin of nucleon. When the spins of two nucleons are parallel the forces between them are strong. If the spins are antiparallel, the forces are weak.
iv) These forces will not at along in line joining the nucleons  ie they are non-central forces.
v) Nuclear forces are due to the result of the exchange of ' π ' mesons between the nucleons.    
Mass defect and Nuclear binding energy:
              It has been found that the mass of a nucleus is less than the sum of the masses of protons and neutrons which constitute the nucleus. This difference between the rest mass of a nucleus and the sum of the rest masses of its constituent nucleus is called 'mass defect'.

The mass defect(m) is converted into energy in accordance with Einstein's mass-energy relation '' E = mc2 '', where ' E ' is the energy and ' c ' is the velocity of light in vacuum. This energy gives the necessary potential for the nucleons to bind together and is called 'binding energy'. ie; the mass defect is converted into binding energy. Correspondingly, the same energy must be given to the nucleus, if it is required to break the nucleus into parts. The greater the binding energy per nucleon, the more stable is the nucleus. The maximum value of binding energy per nucleon is 8.8 Mev.
Nuclear fission - It is splitting!
                 In 1938, Otto Hahn and Strass mann were investigating the effect of bombarding uranium with slow neutrons. Madam Meitner and her nephew Frisch in 1939 took lead in the investigations and stated that Uranium nucleus has only small stability of form, and after neutron capture, it divides itself into two nuclei of roughly equal size. The name 'fission' was given to the process as it resembled the process of division of cells in 'biology'.
                 When Uranium -235 is bombarded by neutrons, a uranium nucleus captures a slow neutron, forming an unstable compound nucleus 92U235.

The compound nucleus splits into two nearly equal fragments, Barium (56Ba141) and Krypton (36Kr92) releasing 3 neutrons and energy 'Q'.
* Thus 'Nuclear fission' is the process of breaking up the nucleus of a heavy atom into two or more on less equal fragments, with the release of large amount of energy.
The reaction can be written as
                                    92U235 + 0n1  56Ba141 + 36Kr92 + Q
Energy released in fission:
                In the process of nuclear fission, a large amount of energy is released. The energy is produced, because the original mass of the nucleus of Uranium, before fission is greater than the sum of the masses of the products after fission. This difference between the masses, before and after a fission is converted into energy, according to Einstein's equation E = mc2
* In the process of fission, of one nucleus of Uranium, about 200Mev energy is released. It is found that 1 Kg of Uranium delivers as much energy as the combustion of about 3000 tonns of coal. This energy produced by 1 gm of Uranium in the form of heat corresponds to a continuous power production of about 1000 Kilowatts, which is sufficient to keep ten thousand 100W bulbs burning for a day. The energy is called nuclear or atomic energy.

Nuclear fusion - It is combining:
               It is the synthesis of lighter nuclei. In this process two or more lighter nuclei combine (fuse) together to form a single heavy nucleus
               For example; when two deutrons (four hydrogen nuclei) fuse together, a 'Helium' nucleus is formed and in addition 24 Mev of energy is released. The mass of the single nucleus of Helium formed is always less then the sum of the masses of the individual light nuclei. The difference in mass is converted into large amount of energy, according to massenergy equation of Einstein E = mc2.
                                      1H2 + 1H2    2He4 + 24 Mev of energy.
              For the fusion process to take place the light nuclei must have very high speeds in order to overcome the large coulomb repulsion to obtain these high speeds, the material must be heated to extreemly high temperatures of the order of 107 to 108 K (This is the temperature of the interior of the sun which can be had by the process of fusion)
Which is more harmful Atom bomb or Hydrogen bomb:
              Fusion cannot take place until the fusible material is ignited to high temperatures where as any thermal neutron can start a chain reaction (?) in fusion bomb (Hydrogen bomb) -

- is not limited where as the material in a fission bomb (Atom bomb) to a certain mass(critical mass).
              The energy released in "Nuclear fusion" (Hydrogen bomb) ie 24 Mev., is much less than the energy liberated in the fission Uranium (Atom bomb) which is about 200 Mev., but energy realised per unit mass during fusion of the light nuclei is much greater compared to the fission of Uranium, while the fission of nucleus produces. Thus, Hydrogen bomb is powerful and dangerous. When it is explosed where as the 'Atom bomb' is less powerful when it exploded the after effects are very harmful for future generations radioactive wastes like Barium and Krypton which are harmful the products of fusion are almost harmless.
Chain reaction:
              A chain reaction is a self propagating process in which the number of neutrons multiply rapidly during fission till whole of the fissible material is disintegrated.
Nuclear Reactor:
              A Nuclear Reactor is a device in which enormous amount of nuclear energy is produced by controlled chain reaction. It is some times called atomic reactor or atomic pile. Uncontrolled chain reaction is ''Atom bomb''.

* The first reactor was installed and operated by '' Enrico Fermi '' and his co-workers in Chicago in 1942.
              A nuclear reactor generates energy mainly in the form of heat by means of nuclear fission. The energy it produces can be used for generation of electricity and for peaceful purposes. Reactors are used to convert different elements into radioactive isotopes.
Nuclear reactor will have the following main features:
1. Core:
This is central part of reactor where fissionable material called ' fuel' is kept and fission occurs. The commonly used fissinable materials are :
a) Natural Uranium containing 92.18% of U235 and 0.82% of U238 only one of these isotopes U235 actually undergoes fission.
b) The Thorium isotope Th232
c) Plutonium isotopes Pu239, Pu240 usually the fuel is kept in different Aluminium cars in the form of cylindrical rods placed at some distance apart.
2. Moderator: If is a material used to increase the probability of fission and thus promote a chain reaction.

The function of the moderator is to slowdown the highly energetic neutrons released by U235 during fission,which are again captured by fresh amount of U235 atoms to split in turn. If moderator did not reduce the spread of neutrons many of them would be absorbed by U238 atoms, which do not undergo fission. Heavy water (a compound compossed by oxygen and deuterium), Graphite, Beryllium etc. are used as moderators.
3. Control system: The control system regulates the rate of chain- reaction and prevents it from running spontaneously.This is achieved by pushing control rods into the reactor core. These rods are made of Cadmium or Boron. These rods absorb the neutrons, without under going charge and thus cut down the level of reactivity.
4. The neutron Reflector: By the use of Reflectors on the surface of reactors, Leakage of neutrons can be reduced very much and the neutron flux in the interior can be increased
5. Coolant (Cooling system): The Coolant removes the heat produced by fission as soon as it is liberated in the reactor core. It makes the heat available to other system of nuclear power plant for the generator of electricity etc. This is evolved from the kinetic energy (K.E) of the fission fragments, when they are slowed down in the fissionable substance and by the moderator.

Coolant also controls the temperature of the reactor core and prevents it from getting over heated.
Coolants Used are:
                       a) Air, CO2 (or) He.
                       b) Water (or) Other liquids.
                       c) Certain metals and alloys.
6. Shields (Safety system): To save the workers near the reactor from the harmful effects of various types of radiations like Gamma Rays emitted from the reactor, thick walls of cement, concrete and lead are constructed around the reactor. These are called "Shields".      
              For emergency shut downs tiny balls of "Samarium oxide" a compound of Samarium and oxygen are dropped into the core, which absorb enough neutrons to stop the chain reaction.
Elementary particles:
Elementary particles are the indivisible units of which matter is composed of.
* An "Anti Particle" has to be there for every particle.
The classification of elementary particles is as follows.
                                 i) Photons                             

                                 ii) Gravitons 
                                 iii) Leptons 
                                 iv) Hardons.
             Hardons are further Classified into a) Measons and b) Baryons. These are particles of strong interaction.
* These names have been derived from Greek words "Leptos" (small), "Mesos" (middle) and "Bary" (heavy)
* Baryons are further classified into nucleons (protons and neutrons) and hyperons

Neutrino (ϑ )- travels faster than Light ? ....
               In Radioactive decay it was found that the laws of conservation of angular momentum and energy were obeyed in case of α and γ decay, but not in β decay. To account for this discrepancy, Pauli postulated the existence of a new particle called "Neutrino" (meaning "a little neutral one"), which was confirmed by "Enrico Fermi". It has no charge and mass and hence it cannot interact with matter. So it's detection is very difficult. It has angular momentum and energy. It is capable of penetrating through large thickness of matter without any interaction. Neutrons are generated on large scale in the sun in ''Nuclear Reactions''.
               Very recently, it is found that neutrino travels faster than light if it is proved correct, it challenges ''Einstein's Theory of Relativity''.
"Dirac" and "Botany": 
               The number of elementary particles so far found are more than 200 in number were some one asked the particle physicist Dirac to tell their names the famous scientist told if I would have nemembered their names, I would have studied "Botany"!!

Posted Date : 24-07-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.

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