The ratio of de - Broglie wavelength of `alpha `- particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector `vec(B)` is perpendicular to the velocity vectors of the `alpha` - particle and the proton is

Explanation

Radius of path described is `r="mv"/"qB"`
`rArr mv=qBr`
`lambda=h/"mv"`
`lambda=h/"qBr"`
`rArr lambda_alpha/lambda_p=(q_p r_p)/(q_alpha r_alpha)=1/2`