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  • A proton accelerated from rest through a potential difference of ‘V’ volts has a wavelength  associat

A proton accelerated from rest through a potential difference of ‘V’ volts has a wavelength \lambda associated with it. An alpha particle in order to have the same wavelength must be accelerated from rest through a potential difference of:

Option: 1

 V volt


Option: 2

4V volt


Option: 3

2V volt


Option: 4

V/8 Volt


Answers (1)

best_answer

\lambda =\frac{h}{\sqrt{2m_{p}eV}}\;

\lambda _{\alpha }=\frac{h}{\sqrt{2m_{\alpha }\left ( 2e \right )V\alpha }}

According to question, we have:

\lambda = \lambda_\alpha, 

\therefore\: \frac{h}{\sqrt{2m_{p}eV}}\;=\frac{h}{\sqrt{2m_{\alpha }\left ( 2e \right )V_{\alpha }}}

2\: \times m_{p} \: e \times V =2\times 4\times m_{p}\times 2eV\alpha

\Rightarrow V_{\alpha }=\frac{V}{8}

Therefore, Option(4) is correct

Posted by

Ritika Jonwal

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