Question

State the basic postulates of Bohr’s theory of atomic spectra.

Answer 1

Hint: Bohr’s theory was based on particle-nature of electrons, considering electrons revolve around the nucleus in circular orbit.

Complete step by step solution:
Bohr combined classical and early quantum mechanics concepts to propose a three-postulate theory.
These postulates are:
1. An electron in an atom revolves in certain stable orbits without emitting radiant energy. Each atom has certain definite stable orbits. Electrons can exist in these orbits. Each possible orbit has definite total energy. These stable orbits are called the stationary states of the atom.

2. An electron can revolve around the nucleus in an atom only in those stable orbits whose angular momentum is the integral multiple of \[\dfrac{h}{2\pi }\], where h is the Planck’s constant. If the mass of the electron be m and it is revolving with velocity v in an orbit of radius r, then its angular momentum will be mvr. According to Bohr’s postulate, \[mvr=\dfrac{nh}{2\pi }\]
 where \[n=1,\text{ 2, 3,}...\] and is called the ‘principle quantum number’ of the orbit. This equation is called ‘Bohr’s quantisation condition’.

3. An electron can make a transition from its stable orbit to another lower stable orbit. While doing so, a photon is emitted whose energy is equal to the energy difference between the initial and final states.
If the energy of the initial and final states are \[{{E}_{i}}\] and \[{{E}_{f}}\] respectively, then the frequency v of the photon is given by
\[v=\dfrac{{{E}_{f}}-{{E}_{i}}}{h}\]
This is called ‘Bohr’s frequency condition’.

Note: Bohr’s theory is restricted to hydrogen and hydrogen-like atoms. It gives no information about the wave-nature of electrons. The theory does not explain the distribution of electrons in different orbits.