Dual Nature Of Light Question 135
Question: The energy that should be added to an electron, to reduce its de-Broglie wavelengths from $ {{10}^{-10}} $ m to $ 0.5\times {{10}^{-10}} $ m, will be [KCET (Engg./Med.) 2000]
Options:
A) Four times the initial energy
B) Thrice the initial energy
C) Equal to the initial energy
D) Twice the initial energy
Show Answer
Answer:
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}=4E_{1} $ Hence added energy $ =E_{2}-E_{1}=3E_{1} $
BETA
