Dual Nature Of Light Question 152
Question: A proton and an a-particle are accelerated through a potential difference of 100 V. The ratio of the wavelength associated with the proton to that associated with an a-particle is [DCE 2002; DPMT 2003]
Options:
A) $ \sqrt{2}:1 $
B) $ 2:1 $
C) $ 2\sqrt{2}:1 $
D) $ \frac{1}{2\sqrt{2}}:1 $
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Answer:
Correct Answer: C
Solution:
$ \lambda =\frac{h}{\sqrt{2mQV}}\Rightarrow \lambda \propto \frac{1}{\sqrt{mQ}} $
$ \Rightarrow \frac{{\lambda_{p}}}{{\lambda_{\alpha }}}=\sqrt{\frac{{m_{\alpha }}{Q_{\alpha }}}{m_{p}Q_{p}}} $ $ =\sqrt{\frac{4m_{p}\times 2Q_{p}}{m_{p}\times Q_{p}}}=2\sqrt{2} $
BETA
