Question

An electron , a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e, r_p, r_{\alpha} $ respectively in a uniform magnetic field $B$. The relation between $r_e, r_p, r_{\alpha}$ is :

• A. $r_e > r_p = r_{\alpha}$
• B. $r_e < r_p = r_{\alpha}$
• C. $r_e < r_p < r_{\alpha}$
• D. $r_e < r_{\alpha} < r_p$

Answer 1

Answer: (B)

$r=\frac{\sqrt{2 m k}}{q B}$
$\frac{r_{\alpha}}{r_{p}}=\frac{\sqrt{2 m_{\alpha}}}{q_{\alpha}} \times \frac{q_{p}}{\sqrt{2 m_{p}}}$
$\begin{bmatrix}m_{\alpha}=4 m_{p} \\ q_{\alpha}=2 q_{p}\end{bmatrix}$
$=1$
Mass of electron is least and charge $q_{e}=e$
So, $r_{e}< r_{p}=r_{\alpha}$