A) \[89.61\times {{10}^{-22}}\]
B) \[69.81\times {{10}^{-22}}\]
C) \[18.96\times {{10}^{-20}}\]
D) \[19.86\times {{10}^{-20}}\]
Correct Answer: D
Solution :
\[{{\lambda }_{0}}=250\times {{10}^{-9}}m\]and\[\lambda =200\times {{10}^{-9}}m\] \[E=\frac{1}{2}m{{v}^{2}}=hv-h{{v}_{0}}=\frac{hc}{\lambda }-\frac{hc}{{{\lambda }_{0}}}\] \[=hc\left[ \frac{1}{\lambda }-\frac{1}{{{\lambda }_{0}}} \right]\] \[=6.62\times {{10}^{-34}}\times 3\times {{10}^{8}}\left[ \frac{1}{200}-\frac{1}{250} \right]\times \frac{1}{{{10}^{-9}}}\] \[\therefore \]\[E=19.86\times {{10}^{-20}}J\] Hence, the correction option is [d].
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