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## 11/04/2021

### Bohr's Atomic Model

The atomic model is proposed by Bohr in 1913. The Bohr has made following assumptions.

• The atom has massive positive charged nucleus.
• The electrons revolve round their nucleus in circular orbits. The centrifugal force between electron and nucleus is balanced by electrostatic pull.
• The electron cannot revolve round the nucleus in any arbitrary orbit but certain definite discrete orbits ( stationary orbits ).
• The orbital angular momentum of the electron is equal to an integral multiple of h/2π

Orbital angular momentum = nh / 2π

Where n = Integer

### h = Planck’s constant

• The electrons does not radiate out any electromagnetic energy while revolving in the stationary orbits.
• In other words. the orbits are non-radiating path of the electron.
• When electrons jump from one orbit to another orbit, the atom radiates out energy.
• If E1 and E2 are the energy of the two orbits before and after electron jump, the frequency of the emitted photon is given by

E1 – E2 = hf

ΔE = hf

Where f = Frequency of the emitted radiations

• If I is moment of inertia of an electron and ω is its angular velocity, then

ωI = nh / 2π

( mr2 ) ω = nh / 2π

( mr2 ) ( v / r ) = nh / 2π

mvr = nh /

• The n is called as principal quantum number or Bohr’s circular orbit and it is first, second and third orbits etc…. It fixes the size of allowed orbits

= 1, 2, 3 etc

### Momentum of revolving electron = mvMoment of electron about nucleus = mvr

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