question_answer

When photons of wavelength \[{{\lambda }_{1}}\], are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength \[{{\lambda }_{2}}\]are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength \[{{\lambda }_{3}}.\]is used then find the stopping potential for this case         [JEE ONLINE 09-04-2016]

A) \[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{3}{2{{\lambda }_{1}}} \right]\]

B) \[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{{{\lambda }_{2}}}-\frac{3}{{{\lambda }_{1}}} \right]\]

C) \[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]\]

D) \[\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}-\frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]\]

Correct Answer: A

Solution :

[a]

using these equations