Question

If ${\lambda }_0$ and λ be the threshold wavelength and the wavelength of incident light, the velocity of photo-electrons ejected from the metal surface is:

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

Answer 1

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

We know that:
$K.E=T.E-workfunction$
$\frac{1}{2}m{v}^2=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$
$v=\sqrt{\frac{2hc}{m}\frac{({\lambda }_0-\lambda )}{{\lambda }_0\lambda }}$