Q 12-04-204JEE MainJEE Main 2019 (10 Apr, Shift 1)Medium
A proton, an electron, and a helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let $r_p$, $r_e$ and $r_{He}$ be their respective radii, then,
Answer: (B) $r_e < r_p = r_{He}$
$r = \dfrac{mv}{qB} = \dfrac{\sqrt{2mK}}{qB}$, so at equal $K$, $r \propto \dfrac{\sqrt m}{q}$.
Proton: $\dfrac{\sqrt m}{e}$. Helium nucleus: $\dfrac{\sqrt{4m}}{2e} = \dfrac{\sqrt m}{e}$, the same. Electron: much smaller mass, same charge, so a much smaller radius.
$r_e < r_p = r_{He}$.
Solution by Sreeraj P, M.Sc Physics