Dual Nature Of Light Question 320
Question: Two identical photo-cathodes receive light of frequencies $ f_{1} $ and $ f_{2} $ . If the velocities of the photo electrons (of mass $ m $ ) coming out are respectively $ v_{1} $ and $ v_{2} $ , then [AIEEE 2003]
Options:
A) $ v_{1}-v_{2}={{[ \frac{2h}{m}( f_{1}-f_{2} ) ]}^{1/2}} $
B) $ v_{1}^{2}-v_{2}^{2}=\frac{2h}{m}( f_{1}-f_{2} ) $
C) $ v_{1}+v_{2}={{[ \frac{2h}{m}( f_{1}+f_{2} ) ]}^{1/2}} $
D) $ v_{1}^{2}+v_{2}^{2}=\frac{2h}{m}( f_{1}+f_{2} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
Using Einstein photoelectric equation $ E=W_{0}+{K_{\max }} $ $ hf_{1}=W_{0}+\frac{1}{2}mv_{1}^{2} $ ?..(i) $ hf_{2}=W_{0}+\frac{1}{2}mv_{2}^{2} $ ?..(ii)
$ \Rightarrow h(f_{1}-f_{2})=\frac{1}{2}m(v_{1}^{2}-v_{2}^{2}) $
$ \Rightarrow (v_{1}^{2}-v_{2}^{2})=\frac{2h}{m}(f_{1}-f_{2}) $
BETA
