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### Atomic Physics

Atomic physics (or atom physics) is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change.

**Thomson’s model (1898)**

Atom as a whole is neutral, that is positive charges and negative charges are equal.

The positive charge and the whole mass is uniformly distributed like a cake and electrons embedded appear as cheeriest in the cake. Therefore, it is also called plum pudding model.

It cannot explain a – particle scattering and spectrum of an atom. Leonard in 1903 suggested that atom is made up of tiny particles called electrons and similar tiny particles carrying positive charge. He could not explain why the heating of metals does not eject positively charged particles.

Rutherford’s model

The whole positive charge is concentrated in a small region called nucleus. The size of the nucleus is of the order of 10-15m or I fm.

The electrons revile around the nucleus in circular orbits. The size of an atom is 10-10m. There exists a large empty space around the nucleus.

Atoms are electrically neutral.

Distance of closest approach** r – 2Ze ^{2} / 4??_{0} (KE)**

Impact parameter

**b = Ze**

^{2}cot ?^{2}/ 4??_{0}(KE)It could not explain why the electrons revolving around the nucleus do not fall into the nucleus following a spiral path, that is, it could not explain stability of the atom.

The number of particles scattered through an angle ? is given by

**N (?) a Z**

^{2}/ sin^{4}(?^{2}) (KE)^{2}

**Bohr’s model**

The electrons move around the nucleus in circular orbits.

The orbits are stable called stationary orbits. They have special values of radii such that the angular momentum is quantized that is,

**mvr = nh where h = h/2?.**

The energy is emitted when electrons make a transition from higher to lower orbit and energy is absorbed when electrons jump from lower to higher orbit.

The centripetal force is equal to the electrostatic force.

Radius of nth orbit

**rn = n**

^{2}?_{0}h^{2}/ ?mze^{2}

Binding energy of nth orbit

**E**

_{n}= mZ^{2}e^{4}/ 8?^{2}_{0}h^{2}n^{2}

Sommer feld’s model the electrons revolve around the nucleus in elliptical orbit. The mass of the electron changes with the velocity relectvistically

**M = m**

_{0}/ 1 – v^{2}/ c^{2}

The total angular momentum of an electron is the resultant of orbital angular momentum and radial angular momentum. These two angular momentums are separately quantized.

De – Broglie theory the electrons revolve around the nucleus in stable circular orbits in the form of stationary waves.

Only those circular orbits are possible whose circum ferrous is integral multiple of de- Broglie wavelength associated with the electron, that is,

**2?r – n?**

Velocity of electron in the nth orbit

**Vn = 2?Ze**

^{2}/ 4??_{0}nh = c / 137 z /n = 2.2 x 10^{6}z n**? = 2?e**ch is called fine structure constant =

^{2}/ 4??_{0}**1/137.**

Angular frequency of electron

**= 8?**

^{2}Z^{2}e^{4}m / (4 ??_{0})2 n^{3}h^{3}= 4.159 x 10^{6}Z^{2}/ n^{3 }rads^{-1}

Electric current due to electron motion in nth orbit

**In = 4?Z**

^{2}e^{5}m^{2}/n^{3}h^{3}(4??_{0})^{2}= 1.06 Z^{2}/ n^{3}mA.Magnetic induction produced in the nth orbit

Bn = ?

Bn = ?

_{0}In / 2rn = 8?^{4}Z^{3 }e^{7}m^{2}/ n^{5}h^{5}(4??_{0})^{3}= 12.58 Z^{3}/ n^{5 }Tesla.Magnetic moment produced in the nth orbit

**Mn = ehn / 2 m = ehn / 4?m = 9.26 x 10**Bohr magneton.

^{-24}n Am^{2}= n**KE of electron = e**

PE of electron = - 2KE = e

Binding energy of electron = KE PE = En = - e

^{2}Z^{2}/ 8??_{0}rn = 13.6Z2 / n^{2}eV.PE of electron = - 2KE = e

^{2}Z^{2}/ 4??_{0}rn = - 27.2Z2 / n^{2}eVBinding energy of electron = KE PE = En = - e

^{2}Z^{2}/ 8??_{0}rn = 13.6Z2 / n^{2}eV.**Lonisation potential = En / e = 13.6Z2 / n**

^{2}VRydberg constant

**R = me**

_{4}/ 8?^{2}_{0}ch_{3}= 1.09737 x 10^{7 }m^{-1}

In balmer series

**?(nm) = 364.56n2/n**representation of waves associated with orbital electrons in an atom

^{2}– 4 where n = 3, 4, 5, ……The number of waves N in distance d is

**N = d/?.**

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