A proton and an -particle are accelerated through a potential dif… - Vidyadip

MCQ

A proton and an $\alpha$-particle are accelerated through a potential difference of $100 \mathrm{~V}$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

A
$\sqrt{2}: 1$
B
$2: 1$
✓
$2 \sqrt{2}: 1$
D
$\frac{1}{2 \sqrt{2}}: 1$

✓

Answer

Correct option: C.

$2 \sqrt{2}: 1$

$ \lambda=\frac{h}{\sqrt{2 m Q V}} \Rightarrow \lambda \propto \frac{1}{\sqrt{m Q}} \Rightarrow \frac{\lambda_p}{\lambda_\alpha}=\sqrt{\frac{m_\alpha Q_\alpha}{m_p Q_p}} $
$ =\sqrt{\frac{4 m_p \times 2 Q_p}{m_p \times Q_p}}=2 \sqrt{2}$

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