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A proton, deuteron and an α-particle having the same KE are moving in circular trajectories in a constant magnetic field. If r_p, r_d and r_α denote respectively radius of the trajectories of these particles then

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$r_{α} = r_{p} < r_{d}$

$r_{α} > r_{d} > r_{p}$

$r_{α} = r_{d} < r_{p}$

$r_{p} = r_{d} < r_{α}$

answer is A.

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Detailed Solution

$r = \frac{\sqrt{2 mK}}{Bq}$

$r_{p} : r_{d} : r_{α} = \frac{\sqrt{m_{p}}}{q_{p}} : \frac{\sqrt{m_{d}}}{q_{d}} : \frac{\sqrt{m_{α}}}{q_{α}}$

$r_{p} : r_{d} : r_{α} = \frac{\sqrt{m_{p}}}{e} : \frac{\sqrt{2 m_{p}}}{e} : \frac{\sqrt{4 m_{p}}}{2 e}$

$r_{p} : r_{d} : r_{α} = 1 : \sqrt{2} : 1$

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