Bohr introduced the concept of ” radiation less ” orbits to overcome the difficulty of radiation of energy by an accelerating electron in an atom.

An analysis of the hydrogen spectrum indicated that the energy of an electron in an atom can have certain ‘stationary ‘ values only.

**He postulated that, the electron moves around a nucleus in certain fixed circular paths in which it does not radiate (lose) energy. Therefore, the energy of an electron in a radiationless orbit would remain constant.**

Bohr numbered the corresponding orbits by means of an integer n (1, 2, 3 etc. ). These are known as principal quantum numbers. The electron can not move in any other circular path other than these orbits.

**When an electron absorbs energy, it makes a transition from a lower energy level n _{1} to a higher energy level n_{2} (n_{2} > n_{1}). This process is known as excitation. **

**Similarly when an electron loses (radiates) energy it jumps from a higher to a lower energy level. This is known as de-excitation.**

The difference of energy between any two energy levels (fixed orbits) is emitted as a single photon:

$ \displaystyle \Delta E = h f = \frac{h c}{\lambda} $

Where f & λ are the frequency & wavelength of radiation emitted (or absorbed) during the transition.

**(ii)** Bohr further argued that if the energy of an electron is quantised, the radius of the orbit is also quantised.

This means an electron can not move in circular orbits of arbitrary radius.

If the speed (v) & radius (r) for an orbit remain constant (quantised), then according to the classical mechanics the angular momentum (mvr) must have to be a constant for an orbit.

In order for the theoretical prediction to agree with experimental spectra, Bohr proposed that the angular momentum of an electron in a stationary orbit,

$ \displaystyle L = \frac{n h}{2\pi} $

where n = 1 , 2 , 3 ……. ( n = principal quantum numbers)

Angular momentum of an electron in an orbit is integral multiple of , where h = Planck’s constant

= 6.63 × 10^{-34} J.s.

Using mechanics & electrodynamics, Bohr calculated the expressions for radius, orbital speed, potential energy, kinetic energy, total energy, frequency of revolution etc. in terms of the electronic mass m, electronic charge e, Planck ‘s constant h etc.

### Also Read :

∗ Rutherford experiment & Observations ∗ Rutherford experiment : Conclusion & Limitations ∗ Bohr’s Stationary Radii & Orbital Speed ∗ Energy of the electron in nth orbit ∗ Origin of Spectra |