a
\({{\text{m}}_p} = {\text{m}}\)               \({{\text{q}}_{\text{p}}} = {\text{q}}\)               \({{\text{k}}_{\text{p}}} = {\text{qV}} = {\text{k}}\)

\({{\text{m}}_\alpha } = {\text{4m}}\)               \({q_\alpha } = 2q\)               \({k_\alpha } = 2qV = 2k\)

Radius of circular path,

\(r=\frac{m v}{q B}=\frac{\sqrt{2 k m}}{q B}\)

\( \Rightarrow \) \(\frac{{{r_p}}}{{{r_\alpha }}} = \frac{1}{{\sqrt 2 }}\)