Question

Sommerfeld extended Bohr’s theory to explain the fine spectrum of H atom.
A.True
B.False

Answer 1

Hint: Bohr’s model does not explain the fine structure of spectral lines. Fine structure of the spectral line is obtained when spectrum is viewed by a spectroscope of high resolving power.

Complete answer:
The important postulates on which Bohr’s atomic model was based are the following:
First postulate: Atoms have a nucleus and it is the nucleus where all protons and neutrons are present. Also, the size of the nucleus is very small and it is located at the centre of the atom.
Second postulate: Electrons are negatively charged and they revolve around the nucleus with the circular path. The attraction force between the nucleus and electron is equal to the centrifugal force on the electron.
Third postulate: The electrons can revolve only in those orbits in which angular momentum of electron is integral multiple of \[\dfrac{{\text{h}}}{{2\pi }}\] , it can be given as: \[{\text{mvr}} = \dfrac{{{\text{nh}}}}{{2\pi }}\] .
Fourth postulate: Stationary orbits are those in which electrons can revolve and they are named stationary because in these orbits the energy of the electron is constant.
Fifth postulate: Each stationary orbit is associated with a definite amount of energy therefore these orbits are also called as energy levels.
Sixth postulate: the emission or absorption of energy can only occur when the electron jumps from one stationary state to another. Energy is absorbed when an electron jumps from inner to outer orbit and is emitted when the electron moves from outer to inner orbit.
Limitation of Bohr’s model: this do no explain the spectrum of multi electron atom, why the angular momentum of electron is equal to \[\dfrac{{{\text{nh}}}}{{2\pi }}\] , do not explain the fine structure of spectral lines and do not explain the splitting of spectral lines in the presence of magnetic and electric field.
According to Sommerfeld, electrons do not revolve in circular paths but rather revolve in the elliptical orbits. He also gave the idea of sub orbits or sub levels which mean the atomic orbits proposed by Bohr can be further split into an orbital. These cleared the fine spectrum of Bohr’s theory. Thus, Sommerfeld extended Bohr’s theory to explain the fine spectrum of the H atom.

Thus, the correct option is A.

Note:
Bohr’s atomic model was based on quantum theory of radiation and classical law of physics. It was applicable only for single electron species and it was based on the particle nature of electrons.