If $\lambda_0$ and $\lambda$ are respectively the threshold wavelength and wavelength of incident light, the…
If $\lambda_0$ and $\lambda$ are respectively the threshold wavelength and wavelength of incident light, the velocity of photo electrons ejected from the metal surface is
$\sqrt{\frac{2 h c}{m}\left(\frac{\lambda_0-\lambda}{\lambda \lambda_0}\right)}$
$\sqrt{\frac{2 h c}{m}\left(\lambda_0-\lambda\right)}$
$\sqrt{\frac{2 h c}{m}\left(\frac{1}{\lambda_0}-\frac{1}{\lambda}\right)}$
Solution
According to Eistein's equation of photoelectric effect.
$\begin{aligned}
& h v=h v_0+K \cdot E \\
& \therefore \quad \frac{1}{2} m v^2=h\left(v-v_0\right)=\frac{h c}{\lambda}-\frac{h c}{\lambda_0} \\
& \text { or, } \quad v^2=\frac{2 h c}{m}\left(\frac{1}{\lambda}-\frac{1}{\lambda_0}\right) \\
& v=\sqrt{\frac{2 h c}{m}\left(\frac{\lambda_0-\lambda}{\lambda \lambda_0}\right)}
\end{aligned}$