Chemistry deals with structure, composition, properties of matter. Matter can be classified into mixtures, compounds and elements. All of them consists molecules and atoms. According to Greek philosophers atoms are fundamental blocks of the matter. The word atom was derived from Greek word "atomio", which means "non-divisible". According to Daltons atomic theory, atoms can be further divided into sub atomic particles like protons, electrons and neutrons. This theory successfully explained the law of Conservation of mass, Law of Constant composition and law of multiple proportion.

Electron was discovered by J.J. Thomson in cathode rays experiment in a discharge tube. Proton was discovered by Goldstein in canal ray's experiment. Neutron was discovered by James Chadwick by bombarding a thin sheet of Be by α -particles. Experimental observations suggested few atomic models to explain the structure of atom i.e., distribution of these charged particles in an atom.

According to Thomson watermelon model of atom, positive charge is uniformly distributed in an atom just like red mass present in watermelon and the electrons are embedded in it (like seeds). Rutherford's nuclear model of atom resembles the solar system. In which nucleus is compared with Sun and electrons with the revolving planets.  This model could not explain the stability of atom and electronic structure of atom. 
 Maxwell suggested that when electrically charged particle moves under acceleration, electro-magnetic waves are produced. They are propagating in perpendicular directions in one other, can move in vacuum. The spectrum of electromagnetic radiation consists γ-rays, X-rays, u.v. rays visible I.R., microwave, radio and long radio waves.

The distance between two successive crests or troughs in a wave is called wavelength (λ). The number of waves passing through a point in one second is called frequency (ν). The number of waves present in Unit length are called wave number (). The height of the crest or depth of a trough is called amplitude.

Velocity of light (c) = ν . λ        
Light is electromagnetic radiation which possesses both the particle nature (black body radiation & photo electric effect) and wave nature (diffraction and interference). Particle nature of electromagnetic radiation was explained by Plank's quantum theory.

Plank's quantum theory:

Black body radiation was successfully explained by Max Plank in 1900. A hallow metallic sphere coated inside with platinum black with a fine hole acts as black body. Which is a perfect absorber and perfect radiator of energy. Radiation is associated with energy. The energy is emitted or absorbed by a body discontinuously in the form of a small packet called "quantum". Energy is directly proportional to the frequency of radiation.   E   ν

                       E = h ν

Propagation of radiant energy in the form of quanta is called "quantization of energy".

          E = n . h ν (n = integer)

Curves are obtained by plotting 'E' against 'λ'. As the temperature increases, the peak of the curve shifts to lower λ.

At a given temperature, the intensity of the radiant energy increases with the λ, reaches maximum and then decreases.

        In 1905, Einstein replaced the word quantum by "photon". He explained photo electric effect. Emission of electrons from a clean metal surface when light (photons) with suitable λ falls on it is called "photo electric effect". It is readily exhibited by alkali metals.

                  h ν = W + K.E.

                  h ν = energy of photon

                  W = work function

                  K.E. = Kinetic energy of emitted electron.

The series of coloured bands obtained by splitting of electromagnetic radiation when it is passed through prism is called "spectrum". The spectrum which is produced due to excitation and de-excitation of electrons of atoms is called "line spectrum". This spectrum has sharp, well defined and distinct lines. If the spectrum is produced by molecules, it is called "Band spectrum", which has closely spaced lines (bands). The study of emission or absorption spectra is known as "spectroscopy" and is useful in chemical analysis.

"Absorption spectrum" is produced due to excitation of atoms or molecules or ions, when they absorb energy. This spectrum consists dark lines on a bright background. "Emission spectrum" is produced due to emission of light by excited ions or atoms or molecules. This spectrum consists of bright lines on a dark background.

Bohr's Model of Atom

Bohr's model of atom is a modification of Rutherford's model. It is based on Plank's quantum theory and hydrogen spectrum.
Postulates:      ¤ Electrons revolve round the nucleus in fixed, circular paths called 'orbits'.

¤ Orbits are denoted by 1, 2, 3, 4... or K, L, M, N ...

¤ Each orbit is associated with definite amount of energy called Energy levels.

¤ Electrons neither emit nor absorb energy when they revolve in a orbit called 'stationary orbit'.

¤ As 'n' value increases the size, energy of orbit increases. The angular momentum of an electron is integral multiple of  i.e. mvr = 

¤ Energy absorbed or emitted by electron is given by ∆E = E₂ - E₁ = hν.

Explanation of emission spectrum of H-atom:

Of all the atomic spectra, the hydrogen spectrum is the simplest spectrum. H atom has only one electron, but it gives 5 series of spectral lines. When H2 gas is heated or exposed to light or subjected to electric discharge, electrons of different H atoms get excited to different higher orbits and deexcites to different lower orbits in different manner with the emission of energy and give 5 series of spectral lines. λ of a spectral line in H atom can be calculated by using Rydberg's equation

    

         R = 2π² me⁴/ch³

Limitations of Bohr's model

¤ This theory explains only spectra of H and H like species.

¤ This theory could not explain fine structure of H- spectrum.

¤ This model failed to explain Zeeman effect and Stark effect.

¤ This theory could not explain the ability of atoms to form molecules by chemical bonds.

¤ This model failed to explain why angular momentum should always be an integral multiple of 

Derivation of equation for radius of n^th orbit (r_n):

H atom has 1 proton in its nucleus with +e charge. An electron with -e charge revolves round the nucleus in a circular orbit of radius 'r'. As per Coulomb's law, electrostatic force of attraction between the nucleus and the electron is given by centripetal (attractive) force 

To make atom stable, an equal and opposite centrifugal force must act away from the nucleus

by substituting (4) in (3)

   = 0.529 × 10^-8 n² cm

Derivation of equation for Energy of electron in nth orbit    

Quantum Mechanical Model of Atom

Modern theory of atomic structure was proposed on the basis of quantum mechanics. The branch of science that takes into account this dual behaviour of matter is called quantum mechanics. It was developed by Heisenberg and Schrodinger. Quantum mechanical model of atom is the picture of the structure of the atom. Main features of this model are:

¤ The energy of electrons in atoms is quantized.

¤ The existence of quantized electronic energy levels is a result of the wave nature of electrons and also allowed solutions of Schrodinger wave equation.

¤ It is impossible to know exact position and momentum of an electron in an atom can not be determined simultaneously (Heisenberg uncertainty principle)

                                             ∆x . ∆p ≥  

¤ Atomic orbital is the wave function Ψ for an electron in an atom. Ψ Must be finite, continuous and single value.

¤ The probability of finding electron at a given point in an atom is proportional to Ψ² (orbital).

¤ Schrodinger wave equation gives the probability of finding electron around nucleus

          

            Ψ = wave function, m = mass of electron

             E = total energy of electron, U = potential energy of e-

De Broglie Theory

All micro particles moving with high velocities are associated with wave characteristics

           E = hν (plank's quantum theory) .............. (1)

           E = mc² (Einstein's theory) ........... (2)

            from (1) & (2)

            mc² = hν =  

         

    If circumference of the electron orbit 2 πr = nλ, electron wave is in phase. If 2πr ≠ nλ, electron wave is not in phase.

Quantum Numbers

A set of numbers used to provide complete description of an electron (energy and its complete address) in an atom are called quantum numbers. Four quantum numbers, i.e. Principal, Azimuthal, Magnetic and Spin quantum numbers are required for this purpose.

1. Principal Quantum number (n):

     ¤ It was proposed by Neils - Bohr.

     ¤ Is is denoted by 'n'.

     ¤ n values can be denoted by K, L, M, N... or 1, 2, 3, 4...

     ¤ The size and energy of the orbit increases with the increase of n.

     ¤ It also represents the distance between the electron and nucleus.

     ¤ The number of electrons present in an orbit = 2 n².

     ¤ Angular momentum of an electron in an orbit =  

     ¤ This quantum number indicates the size and energy of the orbit.

2. Azimuthal Quantum number (l):

¤ It was proposed by sommerfeld.

¤ It is denoted by 'l'.

¤ The values of l = 0, 1, 2, 3... (n-1)

¤ It represents sub - shells (s, p, d, f) in a shell.

¤ The number of subshells in an orbit are equal to 'n'.

¤ When l = 0, 1, 2, 3... electron belongs to the subshell s, p, d, f respectively.

¤ The shapes of s, p, d, f orbitals are spherical, dumb-bell, double dumb-bell and four fold dumb-bell.

¤ Energy of these sub-shells: s < p < d < f.

¤ The number of electrons present in a sub-shell are equal to 2(2l+1), i.e. 2 electrons in s, 6 electrons in p, 10 electrons in d and 14 electrons are present in f sub-shells.

¤ This quantum number indicates the shape of the orbital.

3. Magnetic quantum number (m):

¤ It was proposed by Lande to explain Zeeman effect.

¤ It is denoted by m.

¤ m values are ranging from -l to 0 to +l.

¤ m has (2l + 1) values.

¤ m values are 1, 3, 5, 7 if l values are 0, 1, 2, 3 respectively.

¤ The energy of all the orbitals present in a sub-shell is same.

¤ m value indicates the total number of orbitals in a sub-shell.

¤ The no. of orbitals in s, p, d, f sub-shells are 1, 3, 5, 7 respectively.

     ¤ No. of orbitals in any orbit = n²

¤ This quantum number indicates orientation of an orbital.

4. Spin quantum number (s):

¤ It was proposed by George Uhlenbeck and Samuel Goudsmith.

¤ It is denoted by s.

¤ Electron can spin on its own axis either in clock wise direction (is denoted by +  or ↑) &  in anti clock wise direction (is denoted by -  or ↓). 

¤ For every value of m, there can be two 's' values.

¤ Maximum number of electrons in an orbital = 2 (one electron makes clock wise spin, other electron makes anti clock wise spin).

¤ The difference between the 2 spin quantum numbers is 1.

¤ Spin quantum number indicates the spin of the electron in an orbital.

Shapes of Atomic Orbitals

       Atomic orbital is the space around the nucleus where the probability of finding an electron (Ψ2) is maximum (95%). The probability of finding electron within the radial space around the nucleus is called radial probability distribution. It can be calculated by using the formula 4πr² dr Ψ². The radial space at which the radial probability of finding electron is Zero is called "node" or "radial node" or "nodal region". It is the space between two similar orbitals. The number of nodes are equal to n-l-1. The probability of finding electron at the nucleus is Zero and is called "nodal point". The plane passing through this point is called "nodal plane" (or angular node). The number of nodal planes of orbital are equal to "l". The total number of radial nodes and angular nodes for any orbital are equal to (n -1). The nodal planes of p_x orbital is yz, p_y is zx, p_z is xy, d_xy are yz & zx, d_yz are zx & xy, d_zx are yz & xy and d_x2-_y2 are yz & zx.

The shape of the orbital depends on n & l values.

s - orbital: The shape of s orbital is spherical. Its

l = 0. It is non directional orbital.

p - orbital: The shape of p orbital is dumb-bell and having 2 lobes. Its l = 1. These orbitals are degenerate orbitals and are directional. If they orient along x, y, z axes they are called p_x, p_y, and p_z orbitals.    

Orbital:    p_x             p_y      p_z

m value:   ±1            ±1      0

p orbital has one nodal plane.

d-orbital: The shape of d orbital is double dumb-bell and having 4 lobes. Its l = 2.

d_xy, d_yz, d_zx orbitals are oriented in between the axes. Where as d_x2-_y2, d_z2 orient along the axes.

Orbital:     d_xy    d_yz     d_zx     d_x2-_y2         d_z2

m value:    ±2       ±1      ±1        ±2              0

f-orbital: The shape of f orbital is 4 fold dumb-bell and having 8 lobes. Its l = 3. Seven f orbitals are f_x3, f_y3, f_z3, f_xyz, f_x (y² - z²), f_y (z² - x²) and f_z (x² - y²).

    The energy order of the orbital is s < p < d < f.

Electronic Configuration

The distribution of electrons in different orbitals present in an atom of an element is called "electronic configuration". It is governed by Aufbau principle, Paulis exclusion principle and Hund's rule.

Aufbau Principle

Electrons enter into various atomic orbitals in an atom in increasing order of the energy of atomic orbitals. Energy sequence of atomic orbitals can be remembered either by Moeller's diagram or by (n + l) rules. Electron first enters into atomic orbital whose n + l value is lowest. If n + l values are same for different atomic orbitals, orbital with lowest n value will be filled first. The order of filling electrons is

1s < 2s < 2p_x = 2py = 2p_z< 3s < 3p_x = 3p_y = 3p_z< 4s < 3d_xy = 3d_yz = 3d_zx = 3d_x2-_y2 = 3d_z2 < 4p_x = 4p_y = 4p_z< 5s <...........

Pauli's exclusion principle:

No two electrons in an atom will have the same set of values for 4 quantum numbers. Mean while an orbital can accommodate maximum of 2 electrons with opposite spins.
                                    n     l     m         s

eg: He 1st electron: 1      0    0    +     
            2nd electron: 1     0     0    -   

Hund's rule of maximum multiplicity:

Pairing of electrons in atomic orbitals of the same sub-shell takes place only after filling each orbital with one electron. The pairing of electrons in p, d, f orbitals start with the entry of 4^th, 6^th and 8th electron respectively.

By keeping all these 3 rules in mind one can write electronic configuration by nl^x method.

Stability of completely filled and half filled sub shells:

Sub-shells either half filled or completely filled are more stable due to lowering of energy (due to the exchange energy) and symmetrical distribution of electrons. More repulsions are observed when two electrons are with parallel spins.