Q. If $\lambda _{ο}$ and $\lambda $ be the threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is :

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A

$\sqrt{\frac{2 hc}{m} \left(\frac{\left(\lambda \right)_{ο} - \lambda }{\lambda \left( \lambda \right)_{ο}}\right)}$

B

$\sqrt{\frac{2 hc}{m} \left(\left(\lambda \right)_{ο} - \lambda \right)}$

C

$\sqrt{\frac{2 h}{m} \left(\left(\lambda \right)_{ο} - \lambda \right)}$

D

$\sqrt{\frac{2 h}{m} \left(\frac{1}{\left(\lambda \right)_{ο}} - \frac{1}{\lambda }\right)}$

Solution:

Einstein photo Electric Equation
$\text{hν} - \text{hν}_{0} = \frac{1}{2} \text{mV}_{\text{max}}^{2}$
$\text{h} \frac{\text{C}}{\lambda } - \text{h} \frac{\text{C}}{\lambda _{0}} = \frac{1}{2} \text{mV}_{\text{max}}^{2}$
$\frac{2 \text{hC}}{\text{m}} \left(\frac{1}{\lambda } - \frac{1}{\left(\lambda \right)_{0}}\right) = \text{V}_{\text{max}}^{2}$
$\left(\text{V}\right)_{\text{max}} = \sqrt{\frac{2 \text{hC}}{\text{m}} \left(\frac{\left(\lambda \right)_{0} - \lambda }{\lambda \left( \, \, \, \lambda \right)_{0}}\right)}$

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