Question

A proton, a deutron and an $\alpha$-particle with same kinetic energy enter perpendicularly in a uniform magnetic field, then the ratio of radii of their circular paths is

• A. $1:1:\sqrt{2}$
• B. $\sqrt{2}:1:1$
• C. $1:\sqrt{2}:1$
• D. $1:2:\sqrt{2}$

Answer 1

The correct option is C $1:\sqrt{2}:1$

We know that,

Mass of $m_p=m{m}_D=2m_{\alpha }=4m$

$\because r=\frac{\sqrt{2mE}}{Bq};\therefore r\propto \frac{\sqrt{m}}{q}$

Hence, $r_p:r_d:r_{\alpha }=\frac{\sqrt{m_p}}{q_p}:\frac{\sqrt{m_d}}{q_d}:\frac{\sqrt{m_{\alpha }}}{q_{\alpha }}$

$=\frac{\sqrt{m}}{e}:\frac{\sqrt{2m}}{e}:\frac{\sqrt{4m}}{2e}=1:\sqrt{2}:1$