A proton and an α -particle are accelerated through the same potential difference V . The ratio of their de-Broglie wavelength is

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A proton and an

α

-particle are accelerated through the same potential difference

V .

The ratio of their de-Broglie wavelength is

PhysicsDual Nature of MatterNEET

Options:

A $\sqrt{2}$
B $2 \sqrt{2}$
C $\sqrt{3}$
D $2 \sqrt{3}$

Solution:

2591 Upvotes Verified Answer

The correct answer is:

2 \sqrt{2}

λ = \frac{h}{\sqrt{2 m q V}}

As

V

is same.

λ \propto \frac{1}{\sqrt{m q}}

\frac{λ_{p}}{λ_{α}} = \frac{\sqrt{m_{α} q_{α}}}{\sqrt{m_{p} q_{p}}} = \frac{\sqrt{{4 m}_{p} \times 2 q_{p}}}{\sqrt{m_{p} q_{p}}}

= 2 \sqrt{2}

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