Atomic Structure Question 422

Question: If a proton and $ \alpha $ -particle are accelerated through the same potential difference, the ratio of de-Broglie wavelengths $ {\lambda_{p}} $ and $ {\lambda_{\alpha }} $ is

Options:

A) 3

B) $ 2\sqrt{2} $

C) 1

D) 2

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ {\lambda_{p}}=\frac{h}{\sqrt{2eVm_{p}}}; $

$ {\lambda_{H{e^{2+}}}}=\frac{h}{\sqrt{2\times 2eV{m_{H{e^{2+}}}}}}=\frac{h}{\sqrt{2\times 2eV\times 4m_{p}}} $
$ \therefore \frac{{\lambda_{p}}}{{\lambda_{H{e^{2+}}}}}=2\sqrt{2} $



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