A proton (mass $= M$ ) and a $α -$ particle (mass $= 4 M$ ) are sent into an electric field. The ratio of accelerations of the proton and $α -$ particle is :

1 : 1

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1 : 2

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2 : 1

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4 : 1

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Solution

The correct option is B $2 : 1$
We know that proton $q_{p} = + e, m_{p}$
$α - p a r t i c l e q_{α} = + 2 e, m_{α} = 4 m_{p}$
force acting on proton $= e E$
$∴$ acceleration $a_{p} = \frac{E e}{m_{p}}$

force acting on $α - p a r t i c l e$ $= 2 e E$
$∴ a_{α} = \frac{E (2 e)}{4 m_{p}}$

$a_{p} : a_{α} = \frac{E e}{m p} : \frac{E e}{2 m p}$
$= 2 : 1$

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