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  • A proton and an \alpha - particle ( with their masses in the ratio of 1 : 4 and charges in the ratio 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (

A proton and an \alpha - particle ( with their masses in the ratio of 1 : 4 and charges in the ratio 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicualr to their velocities , the ratio of the radii r_{p} : r_{\alpha} of the circular paths described by them will be :

Answers (1)

Given

\frac{M_{p}}{M_{\alpha }}=\frac{1}{4}

\frac{Q_{p}}{Q_{\alpha }}=\frac{1}{2}

Potential Difference=V

kE=q\Delta V

r=\frac{\sqrt{2mq\Delta v}}{qB}

r\alpha \sqrt{\frac{m}{q}}

\frac{r_{p}}{r_{\alpha }}=\sqrt{\frac{m_{p}}{m_{\alpha }}}\times \sqrt{\frac{q_{\alpha }}{q_{p}}}

\frac{r_{p}}{r_{\alpha }}=\sqrt{\frac{1}{4}}\times \sqrt{2}=\frac{1}{\sqrt{2}}

Posted by

Safeer PP

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