Suppose, the electron in a hydrogen atom makes transition from *n* = 3 to *n* = 2 in 10^{−8} s. The order of the torque acting on the electron in this period, using the relation between torque and angular momentum as discussed in the chapter on rotational mechanics is

#### Options

10

^{−34}^{ }N m10

^{−24}^{ }N m10

^{−42}^{ }N m10

^{−8}^{ }N m

#### Solution

10^{−42}^{ }N-m

The angular momentum of the electron for the *n*th state is given by

`L_n = (nh)/(2pi)`

Angular momentum of the electron for *n* = 3,

n = 3 , `L_i = (3h)/(2pi)`

Angular momentum of the electron for *n* = 2, `L_f= (2h)/(2pi)`

The torque is the time rate of change of the angular momentum.

Torque `tau = (L_f - L_i)/t`

= `((2h//2pi)-(3h//2pi))/10^-8`

= `-(h//2pi)/((10^-8)`

= `(-10^-34)/10^-8 ..............[∴ h/(2pi) ≈ 10^-34 J -s ]`

= -10^{-42} N - m

The magnitude of the torque is `10^-42 N.m`