Question

When photons of wavelength ${\lambda }_1$ are incident on an isolated sphere suspended by an insulated thread, the corresponding stopping potential is found to be $V$. When photons of wavelength ${\lambda }_2$ are used, the corresponding stopping potential was thrice the above value. If light of wavelength ${\lambda }_3$ is used, calculate the stopping potential for this case.

• A. $\frac{hc}{e}\left[\frac{1}{{\lambda }_3}+\frac{1}{2{\lambda }_2}-\frac{1}{{\lambda }_1}\right]$
• B. $\frac{hc}{e}\left[\frac{1}{{\lambda }_3}+\frac{1}{2{\lambda }_2}-\frac{3}{2{\lambda }_1}\right]$
• C. $\frac{hc}{e}\left[\frac{1}{{\lambda }_3}+\frac{1}{{\lambda }_2}-\frac{1}{{\lambda }_1}\right]$
• D. $\frac{hc}{e}\left[\frac{1}{{\lambda }_3}\frac{1}{{\lambda }_2}-\frac{1}{{\lambda }_1}\right]$

Answer 1

Answer: (B)

$\frac{hc}{e}\left[\frac{1}{{\lambda }_3}+\frac{1}{2{\lambda }_2}-\frac{3}{2{\lambda }_1}\right]$

Stopping potential is $V_0=\frac{hc}{\lambda e}$

$\to V=\frac{hc}{{\lambda }_{1}e}$

$\to 3V=\frac{hc}{{\lambda }_{2}e}$

$\Rightarrow {\lambda }_1=3{\lambda }_2$

Now, Stopping potential for photon of wavelength ${\lambda }_3$ is $\frac{hc}{{\lambda }_{3}e}$

which is also equal to $\frac{hc}{e}\{\frac{1}{{\lambda }_3}+\frac{1}{2{\lambda }_2}-\frac{3}{2{\lambda }_1}\}$