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

Answer

B

Explanation

`|barF|=|(-dU)/(dr)|=momega^(2)r , (mv^(2))/r=momega^(2)r , V=omegar`..(i)
`mvr=(nh)/(2pi),V=(nh)/(2pimr)`...(ii)
(i) & (ii) `rArr r=[(nh)/(2pimomega)]^(1/2) rArr r prop n^(1/2)`
`therefore x=2`