Discussion Forum



1)

Light  of wavelength $\lambda_{ph}$ falls on a  cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is Φ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de-Broglie wavelength of the electrons passing through  the anode is $\lambda_{e}$ . which of the following statement (s) is (are) true ?1122021206_b17.JPG


A) $\lambda_{e}$ increases at the same rate as $\lambda_{ph}$ for $\lambda_{ph}$ < $\frac{hc}{\phi}$

B) $\lambda_{e}$ is approximately halved, if d is doubled

C) $\lambda_{e}$ decreases with increase in $\phi$ and o $\lambda_{ph}$

D) For large potential difference $(V\gg \phi/e),\lambda e$ is approximately halved if V is made four times

Answer:

Option D

Explanation:

$k_{max}=\frac{hc}{\lambda_{ph}}-\phi$

Kinetic energy of electron reaching the anode will be

$K=\frac{h_{c}}{\lambda_{ph}}-\phi+eV$

Now $\lambda_{e}=\frac{h}{\sqrt{2mK}}$

  $= \frac{h}{\sqrt{2m(\frac{hC}{\lambda_{ph}}-\phi+eV)}}$

If eV>>Φ

     $\lambda_{e}= \frac{h}{\sqrt{2m(\frac{hC}{\lambda_{ph}}+eV)}}$

If  $V_{f}=4V_{i}, (\lambda_{e)}f\approx (\lambda_{e)i}$