Dual Nature Of Light Question 336
Question: A photosensitive metallic surface has work function $ hv_{0} $ . If photons of energy $ 2hv_{0} $ fall on this surface the electrons come out with a maximum velocity of $ 4\times 10^{6},m/s $ . When the photon energy is increases to $ 5hv_{0} $ then maximum velocity of photo electron will be [CBSE PMT 2005]
Options:
A) $ 2\times 10^{6},m/s $
B) $ 2\times 10^{7},m/s $
C) $ 8\times 10^{5},m/s $
D) $ 8\times 10^{6},m/s $
Show Answer
Answer:
Correct Answer: D
Solution:
From $ E=W_{0}+\frac{1}{2}mv_{\max }^{2} $
Þ $ 2h{\nu_{0}}=h{\nu_{0}}+\frac{1}{2}mv_{1}^{2} $
Þ $ h{\nu_{0}}=\frac{1}{2}mv_{1}^{2} $ …..(i) and $ 5h{\nu_{0}}=h{\nu_{0}}+\frac{1}{2}mv_{2}^{2} $
Þ $ 4h{\nu_{0}}=\frac{1}{2}mv_{2}^{2} $ …..(ii) Dividing equation (ii) by (i) $ {{( \frac{v_{2}}{v_{1}} )}^{2}}=\frac{4}{1} $
Þ $ v_{2}=2v_{1}=2\times 4\times 10^{6}=8\times 10^{6}m/s $
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