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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.

mv^{2}

=

1

e^{2}

r

4pe_{0}

r^{2}

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

En_{2} - En_{1} = hu

Þ Postulate of radiation

u

= frequency of radiation.

3.

Energy Quantization

Main features of Max Planck's quantum theory:

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

(i) Radius of Bohr Orbit

\ v^{2 }=

rm

… (1)

n^{2}h^{2}

4p^{2}m^{2}r^{2}

… (2)

\ r =

e_{0 }n^{2 }h^{2}

p m e^{2}

… (3)

From equation (3), r_{n} a n^{2}

(ii) Energy of the Electron

P.E. = (- e) ´

e

- e^{2}

4pe_{0}r

K.E.

m v^{2}

2

8pe_{0}r

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

- m e^{4}

8e_{0}^{2}n^{2 }h^{2}

Thus, we see that

E_{n}

a

n^{2}