Question

A proton and an $\alpha$ -particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes $25\, \mu s$ to make $5$ revolutions, then the periodic time for the $\alpha$ -particle would be

• A. $50\, \mu s$
• B. $25\, \mu s$
• C. $10\, \mu s$
• D. $5\, \mu s$

Answer 1

Answer: (C)

Time period of proton $T_{p}=\frac{25}{5}=5 \mu s$
By using $T=\frac{2 \pi\, m}{q B}$
$\Rightarrow \frac{T_{\alpha}}{T_{p}}=\frac{m_{\alpha}}{m_{p}} \times \frac{q_{p}}{q_{\alpha}}$
$=\frac{4 m_{p}}{m_{p}} \times \frac{q_{p}}{2 q_{p}}=2$
$\Rightarrow T_{\alpha}=2 T_{p}=10\, \mu s$