An $α$ -particle, a deuteron and a proton are moving with same momentum in a uniform magnetic field. The ratio of their speeds will be

1:2:4

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4:2:1

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1:1:1

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2:2:4

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Solution

The correct option is B 1:2:4
$p = m v$
Given $p_{α} = p_{d e u t e r o n} = p_{p r o t o n}$
$∴ m_{α} v_{α} = m_{d e u t e r o n} v_{d e u t e r o n} = m_{p r o t o n} v_{p r o t o n}$
$m_{α} : m_{d e u t e r o n} : m_{p r o t o n} = 4 : 2 : 1$
$∴ v_{α} : v_{d e u t e r o n} : v_{p r o t o n} = 1 : 2 : 4$

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