Question

A proton and an $\alpha -$particle enter a uniform magnetic field perpendicular with the same speed. If proton takes $20\mu s$ to make $5$ revolution, then the periodic time for the $\alpha -$particle would be:

• A. $5\mu s$
• B. $8\mu s$
• C. $10\mu s$
• D. $12\mu s$

Answer 1

The correct option is C $10\mu s$

As $T=\frac{2\pi m}{Bq}$

So, $T\propto m$ and $T\propto \frac{1}{q}$

Hence we can say

$\frac{T_{\alpha }}{T_P}=\frac{m_{\alpha }}{m_P}\frac{q_P}{q_{\alpha }}$

$\frac{T_{\alpha }}{5}=\frac{4}{1}\times \frac{1}{2}=2$

$T_{\alpha }=10\mu s$