A) \[2\,\,hc\times {{10}^{6}}J\]
B) \[1.5\,\,hc\times {{10}^{6}}J\]
C) \[hc\times {{10}^{6}}J\]
D) \[0.5\,\,hc\times {{10}^{6}}J\]
Correct Answer: A
Solution :
[a] By using \[\frac{hc}{\lambda }={{W}_{0}}+\frac{1}{2}m{{\upsilon }^{2}}\] \[\Rightarrow \]\[\frac{hc}{400\times {{10}^{-9}}}={{W}_{0}}+\frac{1}{2}m{{\upsilon }^{2}}\] ?(i) and \[\frac{hc}{250\times {{10}^{-9}}}={{W}_{0}}+\frac{1}{2}m{{(2\upsilon )}^{2}}\] ?(ii) On solving (i) and (ii) \[\frac{1}{2}m{{\upsilon }^{2}}=\frac{hc}{3}\left[ \frac{1}{250\times {{10}^{-9}}}-\frac{1}{400\times {{10}^{-9}}} \right]\] ?(iii) From equation (i) and (iii) \[{{W}_{0}}=2hc\times {{10}^{6}}J.\]
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