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? |
$r_α=r_p=r_d$ $r_α=r_p<r_d$ $r_α>r_p>r_d$ $r_α=r_p>r_d$ |
$r_α=r_p<r_d$ |
$R = \frac{mv}{qB} = \frac{\sqrt {2mE}}{qB}$ $ 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$ $\Rightarrow R_p = R_\alpha < R_d$ |