Dual Nature Of Light Question 40
Question: The ratio of momenta of an electron and an $ \alpha - $ particle which are accelerated from rest by a potential difference of 100 V is [MNR 1994; RPET 1997]
Options:
A) 1
B) $ \sqrt{\frac{2m_{e}}{{m_{\alpha }}}} $
C) $ \sqrt{\frac{m_{e}}{{m_{\alpha }}}} $
D) $ \sqrt{\frac{m_{e}}{2{m_{\alpha }}}} $
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Answer:
Correct Answer: D
Solution:
Momentum $ p=mv $ and $ v=\sqrt{\frac{2QV}{m}} $
Þ $ p=\sqrt{2QmV} $
Þ $ p\propto \sqrt{Qm} $
Þ $ \frac{p_{e}}{{p_{\alpha }}}=\sqrt{\frac{e\times m_{e}}{2e\times {m_{\alpha }}}}=\sqrt{\frac{m_{e}}{2{m_{\alpha }}}} $
BETA
