Question

a proton & an alpha particle of the same velocity enter inturn a region of uniform magnetic field, acting perpendicular to their direction of motion. Deduce the ratio of radio of radii of the circular paths described by the particles.

Answer 1

we know, mass of proton, $m_p$ = 1/4 × mass of alpha particle , $m_{\alpha}$

charge on proton, $q_p$=1/2 × charge on alpha particle , $q_{\alpha}$

using formula, $r=\frac{mv}{qB}$

here, v and B are constant terms

so, $r\propto\frac{m}{q}$

so, relation will be ...

$\frac{r_p}{r_{\alpha}}=\frac{m_p}{m_{\alpha}}\frac{q_{\alpha}}{q_p}$

= $\frac{m_p}{4m_p}\frac{2q_p}{q_p}$

= $\frac{1}{2}$

hence, ratio of their radii of the circular path described by the particles is 1 : 2