Q 12-04-017NEETJEE MainMedium
A proton, a deuteron and an alpha particle are each accelerated from rest through the same potential difference and then enter a uniform magnetic field at right angles. The ratio of the radii of their paths is
Answer: (C) $1 : \sqrt{2} : \sqrt{2}$
After acceleration $K = qV$, so $r = \dfrac{\sqrt{2mK}}{qB} = \dfrac{1}{B}\sqrt{\dfrac{2mV}{q}} \propto \sqrt{\dfrac{m}{q}}$.
Proton $\sqrt{m/e}$; deuteron $\sqrt{2m/e}$; alpha $\sqrt{4m/2e} = \sqrt{2m/e}$.
Ratio $1 : \sqrt{2} : \sqrt{2}$.
Solution by Sreeraj P, M.Sc Physics