Question

An electron, a proton , a deuteron and an alpha particle, each having the same speed, are in a region of constant magnetic filed 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 $R_a$. It follows that

• A. $R_e=R_p$
• B. $R_p=R_d$
• C. $R_d=R_{\alpha }$
• D. $R_p=R_{\alpha }$

Answer 1

The correct option is C $R_d=R_{\alpha }$

By using the formula for the radius of circular path:

$r=\frac{mv}{qB}=\frac{v}{\left(\frac{q}{m}\right)}$

$\Rightarrow r\propto \frac{1}{\left(q/m\right)}$

$\because {\left(\frac{q}{m}\right)}_{e^{-}}>{\left(\frac{q}{m}\right)}_{p^{+}}>\{{\left(\frac{q}{m}\right)}_d={\left(\frac{q}{m}\right)}_{\alpha }\}$

$\therefore R_d=R_{\alpha }$