# Bohrâ€™s Atomic Model

Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron revolves around a stationary nucleus of positive charge

*Ze*(called hydrogen-like atom)# Bohrâ€™s model is based on the following postulates

- Bohr postulated that an electron in an atom can move around the nucleus in certain circular stable orbits without emitting radiations.
- Bohr found that the magnitude of the electronâ€™s Angular momentum is quantized i.e.,
*n*= 1, 2, 3, ..... each value of*n*corresponds to a permitted value of the orbit radius.*r*= Radius of_{n}*n*^{th}orbit,*v*= corresponding speed_{n} - The radiation of energy occurs only when an electron jumps from one permitted orbit to another.
*E*_{2}) to lower energy orbit (*E*_{1}), then difference of energies of these orbits, i.e.,*E*_{2}â€“*E*_{1}emits in the form of photon. But if electron goes from*E*_{1}to*E*_{2}it absorbs the same amount of energy.

# Drawbacks of Bohrâ€™s atomic model

- It is valid only for one electron atoms, e.g., H, He
^{+}, Li^{+2}, Na^{+1}, etc. - Orbits were taken as circular but according to Sommerfield these are elliptical.
- Intensity of spectral lines could not be explained.
- Nucleus was taken as stationary but it also rotates on its own axis.
- It could not be explained the minute structure in spectrum line.
- This does not explain the Zeeman effect (splitting up of spectral lines in magnetic field) and Stark effect (splitting up in electric field).
- This does not explain the doublets in the spectrum of some of the atoms like sodium (5890 Ã… and 5896 Ã…).

# Bohrâ€™s Orbits (for Hydrogen and H_{2}-Like Atoms)

Radius of orbit For an electron around a stationary nucleus the electrostatics force of attraction provides the necessary centripetal force, i.e.,

**Fig. 6**

From (i) and (ii), radius of

*n*th orbitâ‡’

**Speed of electron**From the above relations, speed of electron in

*n*th orbit can be calculated as,

where

*c*= speed of light 3 Ã— 10^{8}m/s.