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A proton, a deutron and an alpha particle moving with equal K.E enter perpendicular into a magnetic field. If $r_{p}, r_{d}$ and $r_{a}$ are the respective radii of the circular paths, then the ratios $r_{p} / r_{d}$ and $r_{p} / r_{a}$ are

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a

$1, \frac{1}{\sqrt{2}}$

b

$\frac{1}{2}, 0$

c

$\frac{1}{\sqrt{2}}, 1$

d

$1, \frac{1}{2}$

answer is C.

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Detailed Solution

$r = \frac{\sqrt{2mK}}{Bq} r \propto \sqrt{m} r \propto \frac{1}{q} r_{p,} r_{d} = \sqrt{2} r_{p}, r_{d} = r_{p} \frac{r_{p}}{r_{d}} = \frac{r_{p}}{\sqrt{2} r_{p}} = \frac{1}{\sqrt{2}} \frac{r_{p}}{r_{d}} = \frac{r_{p}}{r_{p}} = \frac{1}{1} = 1 (\frac{1}{\sqrt{2}}, 1)$

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