Question

The moment of momentum of an electron revolving in second Bohr orbit of hydrogen is
A) $2\pi h$
B) $\dfrac{h}{{2\pi }}$
C) $\dfrac{h}{\pi }$
D) $\dfrac{{2h}}{{3\pi }}$

Answer 1

Hint: Use the formula for angular momentum of electron in Bohr’s orbit which relates the angular momentum of an electron with the ${n^{th}}$ Bohr’s orbit and Planck’s constant which can be written as: ${J_n} = \dfrac{{nh}}{{2\pi }}$ .
For the second Bohr orbit, the value of n is $2$. The moment of momentum is also known as angular momentum.

Complete step by step answer:
The moment of momentum is also known as angular momentum. It is denoted by ${J_n}$where $n$ is the nth orbit of a hydrogen atom.
${J_n} = \dfrac{{nh}}{{2\pi }}$
Where, $h = $Plank’s constant.
For the second Bohr orbit, $n = 2$
$\Rightarrow {J_2} = \dfrac{{2h}}{{2\pi }}$
$\Rightarrow {J_2} = \dfrac{h}{\pi }$

Therefore, Option (C) is correct.

Additional information:
Niels Bohr proposed that the moment of momentum or angular momentum of the electron in an atom is quantized. It means that the values of the angular moment are not continuous but discrete. He suggested that the value of angular momentum in each orbit is the integral multiple of $\dfrac{h}{{2\pi }}$, where $h$ is called Planck's constant.
Two models of atomic structure are in use today: the Bohr model and the quantum mechanical model. The quantum mechanical model is based on mathematics. Although it is more difficult to understand than the Bohr model, it can be used to explain observations made on complex atoms.
The quantum mechanical model is based on quantum theory, which says matter also has properties associated with waves. According to quantum theory, it’s impossible to know the exact position and momentum of an electron at the same time. This is known as the Uncertainty Principle.

Note:
This formula for angular momentum can only be used for a hydrogen atom or single electron species in general. This is because Bohr’s atomic model is only applicable to single-electron species.