Question 124: Dual Nature of Matter and Radiation

Question

The ratio of de-Broglie wavelength of an $$\alpha$$ particle and a proton accelerated from rest by the same potential is $$\frac{1}{\sqrt m}$$, the value of m is -

Accepted Answer

Here : $m_\alpha=4 m_P, q_\alpha=2 q_P$, potential $=V$
$\lambda=\frac{h}{\sqrt{2 m q V}}$
So, $\frac{\lambda_\alpha}{\lambda_P}=\sqrt{\frac{2 m_P q_P V}{2 m_\alpha q_\alpha V}}=\sqrt{\frac{m_P \cdot q_P}{4 m_P 	imes 2 q_P}}=\frac{1}{\sqrt{8}}$
$$ \Rightarrow $$ $m=8$

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2

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16

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8

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4

Dual Nature of Matter and Radiation

The ratio of de-Broglie wavelength of an $\alpha particle and a proton accelerated from rest by the same potential is \frac{1}{\sqrt m}$, the value of m is -

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