A) \[\Delta E\]is equal to \[{{\left( \frac{1}{4} \right)}^{th}}\] of initial energy.
B) \[\Delta E\]is equal to \[{{\left( \frac{1}{2} \right)}^{th}}\] of initial energy.
C) \[\Delta E\]is equal to twice of initial energy.
D) \[\Delta E\] is equal to initial energy.
Correct Answer: D
Solution :
From relation, \[{{E}_{1}}=\frac{hc}{\lambda }\] .....(i) and, \[{{E}_{2}}=\frac{hc}{{{\lambda }_{2}}}\] ......(ii) Here, \[{{\lambda }_{2}}=\frac{{{\lambda }_{1}}}{2}\] \[\Rightarrow \] \[{{E}_{2}}-{{E}_{1}}=\frac{hc}{{{\lambda }_{2}}}-\frac{hc}{{{\lambda }_{1}}}\] \[\Rightarrow \] \[\Delta E=\frac{2hc}{{{\lambda }_{1}}}-\frac{hc}{{{\lambda }_{1}}}=\frac{hc}{{{\lambda }_{1}}}\]
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