Question

A Proton And Alpha Particle Are Projected Perpendicular To Field Of Same Velocity The Ratio Of Radius Of Proton To Alpha Particle Is?

Answer 1

✔✅ we know, mass of proton, m_pmp = 1/4 × mass of alpha particle , m_{\alpha}mα 

charge on proton, q_pqp =1/2 × charge on alpha particle , q_{\alpha}qα 

using formula, r=\frac{mv}{qB}r=qBmv 

here, v and B are constant terms 

so, r\propto\frac{m}{q}r∝qm 

so, relation will be ...

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

= \frac{m_p}{4m_p}\frac{2q_p}{q_p}4mpmpqp2qp 

= \frac{1}{2}21 

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