Question

An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_{e}, \, R_{p}, \, R_{d}$ and $R_{\alpha }.$ If follows that

• A. $R_{e}=R_{p}$
• B. $R_{p}=R_{d}$
• C. $R_{d}=R_{\alpha }$
• D. $R_{p}=R_{\alpha }$

Answer 1

Answer: (C)

In perpendicular magnetic field magnetic force provided centripetal force.
By the relation
$qvB=\frac{m v^{2}}{r}$
$ \, r=\frac{m v}{q B} \, r \propto \frac{m}{q}$
Since, $\frac{m}{q}$ ratio for deuteron and $\alpha $ -particle is the same.
$\left(\frac{m}{q} = \frac{4}{2} = 2 \, f o r \, \alpha - p a r t i c l e\right)$
$and(\frac{m}{q}=\frac{2}{1}=2$ for deuteron).
Hence, the radius is the same for both.