The de-Broglie wavelength associated with an electron accelerated through a potential difference is and the de-Broglie

Question

The de-Broglie wavelength associated with an electron accelerated through a potential difference $V$ is $λ_{e}$ and the de-Broglie wavelength associated with a proton accelerated through the same potential difference is $λ_{p}$ . If their corresponding masses are $m_{e}$ and $m_{p}$ , respectively, then the ratio of their de-Broglie wavelengths $(\frac{λ_{e}}{λ_{p}})$ is _______. [2026]

Smart Achievers · Accepted Answer

(1)

$de-Broglie wavelength, λ = \frac{h}{\sqrt{2 m q V}} \propto \frac{1}{\sqrt{m}}$

$(\frac{λ_{e}}{λ_{p}})$

Solution

1 $\sqrt{\frac{m_{p}}{m_{e}}}$

2 $\sqrt{\frac{m_{e}}{m_{p}}}$

3 $\frac{m_{p}}{m_{e}}$

4 ${(\frac{m_{p}}{m_{e}})}^{2}$

Ans.
(1)

$de-Broglie wavelength, λ = \frac{h}{\sqrt{2 m q V}} \propto \frac{1}{\sqrt{m}}$

$So, \frac{λ_{e}}{λ_{p}} = \sqrt{\frac{m_{p}}{m_{e}}}$

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Solution

1 mpme

2 memp

3 mpme

4 (mpme)2