Use Bohr's quantization condition

For an electron revolving in the $n^{\text{th}}$ orbit, Bohr's angular momentum condition is: $mvr = \frac{nh}{2\pi}$

where:

• $m$ = mass of electron
• $v$ = speed of electron
• $r$ = radius of orbit
• $h$ = Planck's constant
• $n$ = orbit number

Express momentum

Linear momentum of the electron is: $p = mv$

From the Bohr condition, $mvr = \frac{nh}{2\pi}$

Dividing both sides by $r$: $mv = \frac{nh}{2\pi r}$

Hence, $p = \frac{nh}{2\pi r}$

Match with the options

• A: $\dfrac{nh}{2\pi r}$ ✓
• B: $\dfrac{nh}{2r}$ ✗
• C: $\dfrac{nh}{2\pi}$ ✗
• D: $\dfrac{2\pi r}{nh}$ ✗

Conclusion

The correct option is: $\boxed{A}$