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  • A proton and an alpha particle are accelerated under the same potential difference. The ratio of de-Broglie wavelengths of the proton and the alpha particle is  <div class='qna

A proton and an alpha particle are accelerated under the same potential difference. The ratio of de-Broglie wavelengths of the proton and the alpha particle is
 

Option: 1

\sqrt{8}


Option: 2

\frac{1}{\sqrt{8}}


Option: 3

1


Option: 4

2


Answers (1)

best_answer

When a charged particle of charge q and mass \mathrm{m} is accelerated under a potential difference \mathrm{V},  let \mathrm{v} be velocity acquired by the particle.  Then

 \mathrm{qV}=\frac{1}{2} \mathrm{mv}^2 \quad \text{or} \quad \mathrm{mv}=\sqrt{2 \mathrm{mqV}}

de Broglie wavelength, \lambda=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}}

\lambda \propto \frac{1}{\sqrt{\mathrm{mq}}} for the same value of \mathrm{V}.

\therefore \frac{\lambda_p}{\lambda_\alpha}=\frac{\sqrt{m_\alpha q_\alpha}}{m_p q_p}=\sqrt{\frac{4 m}{m} \times \frac{2 e}{e}}=\sqrt{8}

Posted by

Ajit Kumar Dubey

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