Question

The angular momentum of electron can have the value(s):
A.$\dfrac{h}{2\pi }$
B.$\dfrac{h}{\pi }$
C.$\dfrac{2h}{\pi }$
D.$\dfrac{5}{2}\dfrac{h}{2\pi }$

Answer 1

We can calculate the Angular momentum of an electron by using the following formula.
mvr = $\dfrac{nh}{2\pi }$ , where n is integer, where v = velocity of electron, n is the orbit in which electron is rotates, m = mass of the electron, r = radius of the nth orbit, and h = Planck’s constant.

Complete answer:
Angular momentum of an electron by using the following formula.
Angular momentum = $\dfrac{nh}{2\pi }$
Substitute n = 1, 2, 3 etc., in the above formula to get angular momentum of the electron in various orbits.
If n = 1, then

& mvr=\dfrac{nh}{2\pi } \\\ & mvr=\dfrac{1h}{2\pi } \\\ \end{aligned}$$ If n = 2, then $$\begin{aligned} & mvr=\dfrac{nh}{2\pi } \\\ & mvr=\dfrac{2h}{2\pi } \\\ & mvr=\dfrac{h}{\pi } \\\ \end{aligned}$$ If n = 3, then $$\begin{aligned} & mvr=\dfrac{nh}{2\pi } \\\ & mvr=\dfrac{3h}{2\pi } \\\ \end{aligned}$$ If n = 4, then $$\begin{aligned} & mvr=\dfrac{nh}{2\pi } \\\ & mvr=\dfrac{4h}{2\pi } \\\ & mvr=\dfrac{2h}{\pi } \\\ \end{aligned}$$ If n = 5, then $$\begin{aligned} & mvr=\dfrac{nh}{2\pi } \\\ & mvr=\dfrac{5h}{2\pi } \\\ \end{aligned}$$ Means by substituting all the integer values we won’t get $$\dfrac{5}{2}\dfrac{h}{2\pi }$$, means option D is wrong. Therefore A, B and C are possible as the angular momentum of electrons in different orbits. **So, the correct options are A, B and C.** **Note:** The postulates of Bohr's Model are as follows: Atoms have a nucleus, and the nucleus contains all the protons and neutrons. The size of the nucleus is very small and it is located at the centre of the atom. The force of attraction between electron and nucleus is equal to the centrifugal force of the electron. Electrons revolve only in those orbits, where the angular momentum (mvr) of the electron is the integral multiple of $$\dfrac{nh}{2\pi }$$.