Question

If ${\lambda }_0$ and $\lambda$ be the threshold wavelength and the wavelength of incident light, the velocity of photoelectrons ejected will be:

• A. $\sqrt{\frac{2h}{m}({\lambda }_0-\lambda )}$
• B. $\sqrt{\frac{2hc}{m}({\lambda }_0-\lambda )}$
• C. $\sqrt{\frac{2hc}{m}\left(\frac{{\lambda }_0-\lambda }{\lambda {\lambda }_0}\right)}$
• D. $\sqrt{\frac{2h}{m}(\frac{1}{{\lambda }_0}-\frac{1}{\lambda })}$

Answer 1

The correct option is C $\sqrt{\frac{2hc}{m}\left(\frac{{\lambda }_0-\lambda }{\lambda {\lambda }_0}\right)}$

Using photo electric equation

$\frac{hc}{\lambda }=\varphi +{KE}_{max}\varphi =\frac{hc}{{\lambda }_0}\frac{hc}{\lambda }=\frac{hc}{{\lambda }_0}+{KE}_{max}hc\left(\frac{{\lambda }_0-\lambda }{\lambda {\lambda }_0}\right)=\frac{1}{2}{mv}_{max}^2{V}_{max}=\sqrt{\frac{2hc}{m}\left(\frac{{\lambda }_0-\lambda }{\lambda {\lambda }_0}\right)}$

(C) is correct option