Question

The angular momentum of the electron in $ {n^{th}} $ orbit is given by
A) $ nh $
B) $ \dfrac{h}{{2\pi n}} $
C) $ n\dfrac{h}{{2\pi }} $
D) $ {n^2}\dfrac{h}{{2\pi }} $

Answer 1

Hint : The electron angular momentum is quantized according to Bohr’s second postulate. We will make use of this relation to relate the angular momentum of the electron with integral multiples of the quantized angular momentum

Complete step by step answer
According to Bohr’s second postulate, the angular momentum of the electron is quantized in integral multiples of $ h/2\pi $ . Hence the angular momentum of the electron in $ {n^{th}} $ orbit is
 $ L = n\left( {\dfrac{h}{{2\pi }}} \right) $ where $ h $ is the Planck’s constant. Here $ n = 1,2,3... $ can only have integer values which means that angular momentum will have values that are integral multiples of $ h/2\pi $ which means it is quantized. The correct choice is hence option (C).
The quantization of angular momentum arises from the reasoning that the electron can revolve around the nucleus in orbits of fixed angular momentum.

Additional Information
Bohr’s second postulate allows the electron to orbit around the nucleus without losing its energy. Otherwise, all accelerated charged particles lose energy in the form of radiation. Bohr postulated that electrons can revolve in orbits with quantized momentum such that they can revolve without losing energy and hence atoms can stay stable and exist for long durations. If Bohr’s second postulate was untrue, atoms wouldn’t be stable and the universe and us as we know wouldn’t exist.

Note
Since the electron can have only fixed angular momentum, it will have a fixed energy depending on the orbit number. As a result, the electron when transitioning from higher energy to lower energy or from lower energy to higher energy will do it in fixed amounts. This has also been proven experimentally where the electron will absorb or gain energy in only fixed intervals on energy.