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Q.

A proton and an $α - particle,$ accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is 10 cm, then that of $α -$ orbit is

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a

20 cm

b

$5 \sqrt{2} cm$

c

$10 \sqrt{2} cm$

d

10 cm

answer is B.

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Detailed Solution

$\begin{array}{l} \frac{1}{2} {mu}^{2} = Q . V \Rightarrow u = \sqrt{\frac{2 QV}{m}}, r = \frac{u}{ω} = \sqrt{\frac{2 QV}{m}} \times \frac{m}{QB} = \frac{1}{B} . \sqrt{\frac{2 Vm}{Q}} \\ ∴ \frac{r_{\propto}}{r_{P}} = \sqrt{\frac{m_{α}}{m_{p}}} . \sqrt{\frac{Q_{P}}{Q_{α}}} = \sqrt{4} . \frac{1}{\sqrt{2}} = \sqrt{2} \Rightarrow r_{\propto} = 10 \sqrt{2} cm \end{array}$

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