Question

In hydrogen atom, an electron makes transition from $n=3$ to $n=2$ state in time interval of $1.2\times {10}^{-8}s$. Calculate the average torque (in Nm) acting on the electron during this transition.

• A. $1.055\times {10}^{-26}$
• B. $4.40\times {10}^{-27}$
• C. $1.7\times {10}^{-26}$
• D. $8.79\times {10}^{-27}$

Answer 1

The correct option is A $1.055\times {10}^{-26}$

Given,

$t=1.2\times {10}^{-8}sec$

By Bohr's model,

Angular momentum,$L=\frac{nh}{2\pi }$

$n=3$, $L_3=\frac{3h}{2\pi }$

$n=2$, $L_2=\frac{2h}{2\pi }$

Torque is the rate of change of angular momentum

$\tau =\frac{L_2-L_3}{t}$

$\tau =\frac{\left(2h/2\pi \right)-\left(3h/2\pi \right)}{t}$

$|\tau |=\frac{h}{2\pi t}$

$|\tau |=\frac{6.65\times {10}^{-34}}{2\times 3.14\times 1.2\times {10}^{-8}}$

$|\tau |=1.055\times {10}^{-26}Nm$

The correct option is A.