Question

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

Answer 1

Hint Use the third postulate that says about the quantization of the angular momentum of an electron in the ${{n}^{th}}$ orbit. The postulate states that the angular momentum is an integral multiple of $\dfrac{h}{2\pi }$ where $h$ is the Planck’s constant.

Complete Step by step solution
The Bohr model of an atom is one of the first atomic models to successfully explain the position of the emission and absorption line in the hydrogen atom. Bohr formulated three postulates to explain his model of the hydrogen atom. The third postulate states that the angular momentum of an electron in an orbit is quantized.
The angular momentum is defined as the product of the moment of inertia of an object and its velocity. It can be viewed as the linear momentum in rotational motion. The angular momentum is given by
$L=mvr$
Here, $m$ is the mass of the electron, $v$ is the velocity of the electron, and $r$ is the radius of the orbit, or it can also be said as the distance of the electron from the nucleus.
Bohr’s third postulate states that the angular momentum of an electron revolving around the nucleus of an atom is quantized. The angular momentum is an integral multiple of $\dfrac{h}{2\pi }$ where $h$ is the Planck’s constant.
That is,
$mvr=n\dfrac{h}{2\pi }$
Here, $n$ has integer values and is the principal quantum number. It denotes the orbit in which the electron resides.

Hence, option (C) is the correct option.

Note
Although Bohr’s atomic model is successful in explaining the position of the absorption and emission lines spectra, it had some errors. One of the major drawbacks of Bohr’s atomic model was that it was primarily used to explain hydrogen atoms.