Question

Assuming photo-emission to take place, the factor by which the maximum velocity of the emitted photo electrons changes when the wavelength of the incident radiation is increased four times, is (assuming work function to be negligible in comparison to $hcl\lambda$)

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

Answer 1

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

Einstein's Photoelectric equation is given as : $\frac{hc}{\lambda }=\varphi +\frac{1}{2}m{v}^2$ (where $\varphi$ = work function , v = velocity of photoelectron, $\lambda$ = wavelength of incident radiation)

as $\frac{hc}{\lambda }>>\varphi \Rightarrow \frac{hc}{\lambda }\approx \frac{1}{2}m{v}^2$

now wavelength is increased by 4 times :

$\Rightarrow {\lambda }_2=4\lambda$

$\Rightarrow \frac{hc}{4\lambda }=\frac{1}{2}m{v}_2^2$

$\Rightarrow \frac{1}{4}\left(\frac{1}{2}m{v}^2\right)=\frac{1}{2}m{v}_2^2$

$v_2^2=\frac{v^2}{4}\Rightarrow v_2=\frac{v}{2}$

so maximum velocity of photoelectrons will be $\frac{1}{2}$ times when wavelength becomes 4 times.