MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Atoms Molecules and Nuclei Page 2

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2.

Bohr Model (for Hydrogen Atom)

First Postulate: An electron in an atom revolves around the nucleus in a circular orbit. The centripetal force is provided by the electrostatic force exerted by the nucleus on the electron.

 mv2 = 1 e2 r 4pe0 r2

Þ Postulate of stationary orbit

Second Postulate: The electron can revolve around the nucleus only in certain allowed orbits those for which the angular momentum of electron is an integral multiple of . These orbits are called stationary orbits.

 mvr = nh 2p

Þ Postulate of quantisation of angular momentum

 where h = Planck's constant n = principle quantum number = 1, 2, 3, 4, …….

Third Postulate: Energy is radiated by the electron only when it jumps from an outer orbit of higher energy to an inner orbit of lower energy. The radiated energy is in the form of photons of energy hu given by

 En2 - En1 = hu

 where h = Planck's constant u = frequency of radiation.

 3. Energy Quantization Main features of Max Planck's quantum theory: Energy is radiated by a source not continuously but in packets or bundles of energy. Each packet is known as 'photon'. Each photon has energy hu. 3.      Energy is absorbed or emitted by a body in integral multiples of hu. (Energy is said to be quantised).

4.

Radius and Energy of Bohr Orbit

1. Find expression for v2 using first postulate
 mv2 = 1 e2 r 4pe0 r2
 \ v2 = 1 e2 4pe0 rm

… (1)

1.
2. Find expression for v2 using 2nd postulate
 mvr = nh 2p
 \ v2 = n2h2 4p2m2r2

… (2)

1.
2. Equating the two values of v2, find expression for 'r'

R.H.S. of (1) = R.H.S. of (2)
 \ r = e0 n2 h2 p m e2

… (3)

From equation (3),  rn a n2

(ii) Energy of the Electron

1. Write expression for P.E. of an electron
P.E. = Electrostatic potential due to nucleus
´ charge on the electron
 P.E. = (- e) ´ 1 e = - e2 4pe0 r 4pe0r
1.
2. Write expression for kinetic energy of an electron using postulate 1.
 K.E. = 1 m v2 = e2 2 8pe0r

3.

Total energy = P.E. + K.E. = E =

- m e4

8e02n2 h2

Thus, we see that

 En a 1 n2

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