A) four times the initial energy
B) thrice the initial energy
C) equal to the initial energy
D) twice the initial energy
Correct Answer: B
Solution :
\[\lambda =\frac{h}{\sqrt{2mE}}\,\,\,\,\Rightarrow \,\,\lambda \propto \frac{1}{\sqrt{E}}\,\,\,\Rightarrow \,\,\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}\,\,=\,\,\sqrt{\frac{{{E}_{2}}}{{{E}_{1}}}}\] \[\Rightarrow \,\,\,\frac{{{10}^{-10}}}{0.5\times {{10}^{-10}}}\,\,=\,\,\sqrt{\frac{{{E}_{2}}}{{{E}_{1}}}}\,\,\,\,\Rightarrow \,\,\,{{E}_{2}}\,=\,\,4{{E}_{1}}\] Hence added energy \[=\,\,{{E}_{2}}-{{E}_{1}}=3{{E}_{1}}\]
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