Proton, deuteron and alpha particles of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$, and $r_α$. Which one of the following relation is correct?
Answer & explanation
Correct answer: option 2
The correct answer is option 2: $r_α=r_p<r_d$
$R = \frac{mv}{qB} = \frac{\sqrt {2mE}}{qB}$
$ R_p = \frac{\sqrt {2m_pE}}{eB}$
$ R_\alpha = \frac{\sqrt {2(4m_p)E}}{2eB} = \frac{\sqrt {2m_pE}}{eB} = R_p$
$ R_d = \frac{\sqrt {2(2m_p)E}}{eB} = \frac{\sqrt {4m_pE}}{eB} > R_p$
$\Rightarrow R_p = R_\alpha < R_d$