Question

The electrons revolve only in the orbit in which

• A. $\mathrm{mvr}>\frac{\mathrm{nh}}{2\mathrm{\pi }}$
• B. $\mathrm{mvr}\ge \frac{\mathrm{nh}}{2\mathrm{\pi }}$
• C. $\mathrm{mvr}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$
• D. $\mathrm{mvr}<\frac{\mathrm{nh}}{2\mathrm{\pi }}$

Answer 1

The correct option is C

$\mathrm{mvr}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$

Out of the infinite number of possible circular orbits around the nucleus, the electron can revolve only in those orbits whose angular momentum$\left(\mathrm{mvr}\right)$ is an integral multiple of$\frac{\mathrm{h}}{2\mathrm{\pi }}$

$\mathrm{mvr}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$
where :
m = mass of the electron
v = velocity of electron
r = radius of the orbit, and
n =1,2,3 ---- number of the orbit.

Conclusion Statement: The electrons revolve only in the orbit in which their angular momentum is$\left(\mathrm{mvr}\right)=\frac{\mathrm{nh}}{2\mathrm{\pi }}$.