Dual Nature Of Light Question 300
Question: When a metal surface is illuminated by light of wavelengths 400 nm and 250 nm, the maximum velocities of the photoelectrons ejected are $ v $ and $ 2v $ respectively. The work function of the metal is (h = Planck?s constant, c = velocity of light in air) [EAMCET (Engg.) 2000]
Options:
A) $ 2,hc,\times 10^{6},J $
B) $ 1.5,hc,\times 10^{6},J $
C) $ hc,\times 10^{6},J $
D) $ 0.5hc,\times 10^{6},J $
Show Answer
Answer:
Correct Answer: A
Solution:
By using $ \frac{hc}{\lambda }=W_{0}+\frac{1}{2}mv^{2} $
$ \Rightarrow \frac{hc}{400\times {{10}^{-9}}}=W_{0}+\frac{1}{2}mv^{2} $ ?..(i) and $ \frac{hc}{250\times {{10}^{-9}}}=W_{0}+\frac{1}{2}m{{(2v)}^{2}} $ ?..(ii) On solving (i) and (ii) $ \frac{1}{2}mv^{2}=\frac{hc}{3}[ \frac{1}{250\times {{10}^{-9}}}-\frac{1}{400\times {{10}^{-9}}} ] $ ?..(iii) From equation (i) and (iii) $ W_{0}=2hc\times 10^{6}J $ .
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