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
  1. $\sqrt{\frac{2 h}{m}\left(\lambda_0-\lambda\right)}$
  2. $\sqrt{\frac{2 h c}{m}\left(\frac{\lambda_0-\lambda}{\lambda \lambda_0}\right)}$
  3. $\sqrt{\frac{2 h c}{m}\left(\lambda_0-\lambda\right)}$
  4. $\sqrt{\frac{2 h c}{m}\left(\frac{1}{\lambda_0}-\frac{1}{\lambda}\right)}$

Solution

According to Eistein's equation of photoelectric effect. $\begin{aligned} & h v=h v_0+K \cdot E \\ & \therefore \quad \frac{1}{2} m v^2=h\left(v-v_0\right)=\frac{h c}{\lambda}-\frac{h c}{\lambda_0} \\ & \text { or, } \quad v^2=\frac{2 h c}{m}\left(\frac{1}{\lambda}-\frac{1}{\lambda_0}\right) \\ & v=\sqrt{\frac{2 h c}{m}\left(\frac{\lambda_0-\lambda}{\lambda \lambda_0}\right)} \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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