Question

A proton and an $\alpha$ -particle, having kinetic energies $K_p$ and $K_{\alpha }$, respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is 2 : 1 The ratio of $K_p:K_{\alpha }$ is:

• A. 1 : 8
• B. 8 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

Answer: (D)

$r=\frac{mv}{qB}=\frac{p}{qB}$
$\frac{m_{\alpha }}{m_p}=4$
$\frac{r_p}{r_a}=\frac{p_p}{q_p}\frac{q_{\alpha }}{p_{\alpha }}=\frac{2}{1}$
$\frac{p_p}{p_{\alpha }}=\frac{2q_p}{q_{\alpha }}=2\left(\frac{1}{2}\right)$
$\frac{p_q}{p_a}=1$
$\frac{K_p}{K_{\alpha }}=\frac{p_p^2}{p_{\alpha }^2}\frac{m_{\alpha }}{m_p}=(1)$ (4)