A deuteron and an alpha particle with the same kinetic energy move in circular paths under the effect of same magnetic field. The ratio of the radii (rd : rα) of their trajectories is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → √2 : 1
A charged particle moving perpendicular to a magnetic field moves in a circle of radius \( r = mv/qB \). For a given kinetic energy the momentum is \( p = \sqrt{2mK} \), so
\( \displaystyle r = \frac{mv}{qB} = \frac{\sqrt{2mK}}{qB} \Rightarrow r \propto \frac{\sqrt{m}}{q} \text{ for the same K and B} \)
A deuteron has mass 2 u and charge e; an alpha particle has mass 4 u and charge 2e.
\( \displaystyle \frac{r_d}{r_\alpha} = \frac{\sqrt{2}/1}{\sqrt{4}/2} = \frac{\sqrt{2}}{1} \)
So \( r_d : r_\alpha = \sqrt{2} : 1 \).