Question

Calculate the radius of the nth orbit

• A. $\sqrt{\frac{\mathrm{nh}}{2\mathrm{\pi eB}}}$
• B. $\sqrt{\frac{\mathrm{nheB}}{2\mathrm{\pi }}}$
• C. $\sqrt{\frac{\mathrm{nhe}}{2\mathrm{\pi B}}}$
• D. $\sqrt{\frac{\mathrm{nhB}}{2\mathrm{\pi e}}}$

Answer 1

The correct option is A

$\sqrt{\frac{\mathrm{nh}}{2\mathrm{\pi eB}}}$

The explanation for the correct answer:-

According to Bohr's quantization rule

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

or $\mathrm{mv}=\frac{\mathrm{nh}}{2\mathrm{\pi r}}$$..........1$

Also, $\mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}}$

or $\mathrm{mv}=\mathrm{rqB}$$..........2$

From 1 and 2,

$\mathrm{rqB}=\frac{\mathrm{nh}}{2\mathrm{\pi r}}\left[\mathrm{q}=\mathrm{e}\right]$

${\mathrm{r}}^2=\frac{\mathrm{nh}}{2\mathrm{\pi eB}}$

$\mathrm{r}=\sqrt{\frac{\mathrm{nh}}{2\mathrm{\pi eB}}}$

So, the radius of the nth orbit is $\mathrm{r}=\sqrt{\frac{\mathrm{nh}}{2\mathrm{\pi eB}}}$.

Hence, option (A) is the correct answer.