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 $100\, V$. 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.

$2 \sqrt{2} : 1$

c
$\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mq} \mathrm{v}_{0}}}$

$\frac{{{\lambda _p}}}{{{\lambda _\alpha }}} = \sqrt {\frac{{{{\rm{m}}_\alpha }{{\rm{q}}_\alpha }}}{{{{\rm{m}}_p}{{\rm{q}}_p}}}} = \sqrt {\frac{{4{{\rm{m}}_p} \times 2{\rm{e}}}}{{{{\rm{m}}_p} \times {\rm{e}}}}} = 2\sqrt 2 $

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