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 :
By using \[\frac{hc}{\lambda }={{W}_{0}}+\frac{1}{2}m{{v}^{2}}\] \[\Rightarrow \frac{hc}{400\times {{10}^{-9}}}={{W}_{0}}+\frac{1}{2}m{{v}^{2}}\] ?..(i) and \[\frac{hc}{250\times {{10}^{-9}}}={{W}_{0}}+\frac{1}{2}m{{(2v)}^{2}}\] ?..(ii) On solving (i) and (ii) \[\frac{1}{2}m{{v}^{2}}=\frac{hc}{3}\left[ \frac{1}{250\times {{10}^{-9}}}-\frac{1}{400\times {{10}^{-9}}} \right]\] ?..(iii) From equation (i) and (iii) \[{{W}_{0}}=2hc\times {{10}^{6}}J\].
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