Question

The angular momentum of an electron present in the excited state of hydrogen is $\dfrac{{1.5h}}{\pi }$. The electron is present in:
(a) Third orbit
(b) Second orbit
(c) Fourth orbit
(d) Fifth orbit

Answer 1

Hint: As before doing a solution, we must firstly explain what angular momentum is. Angular momentum is the product of any body’s mass, velocity and radius. In simple way the property characterising the rotatory inertia of an object about an axis that may or may not pass through the system and in this question we have to find the orbit where the electron is present.

Complete Step by Step Solution:
Given,
Angular Momentum in the excited state of hydrogen = $\dfrac{{1.5h}}{\pi }$
As we know the Formula of angular momentum is,
Angular Momentum=$\dfrac{{nh}}{{2\pi }}$
Here in this all the terms stands for,
n = n is the orbit in which electron is present
h = Planck’s Constant
Where h always provides a constant value and n presents the orbit of the electron and in this question we have to find the orbit of the electron.
By Comparing the value from Angular momentum’s equation, we get
$\dfrac{{1.5h}}{\pi } = \dfrac{{nh}}{{2\pi }}$
Since, by comparing both quantities (using substitution)
n = 3
Hence, the electron present in the Third orbit.
So, the correct answer is: (a) Third Orbit

Note: There are 2 special types of angular momentum of an object: the spin angular momentum is the angular momentum about the object centre of mass while the orbital angular momentum is the angular momentum about the chosen centre of rotation.