Question

Assuming photoemission to take place, the factor by which the maximum velocity of the emitted photoelectrons changes when the wavelength of the incident radiation is increased four times, is

• A. 4
• B. $\frac{1}{4}$
• C. 2
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

$\frac{hc}{\lambda }=W_0+\frac{1}{2}m{v}_{max}^2$
Assuming W_0 to be neglibigle in comparison to $\frac{hc}{\lambda }$
ie., $v_{max}^2\propto \frac{1}{\lambda }\Rightarrow v_{max}\propto \frac{1}{\sqrt{\lambda }}$
(On increasing wavelength $\lambda$ to $4\lambda ,v_{max}$ becomes half).