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

Options

A. `1`
B. `(1)/(4)`
C. `(1)/(2)`
D. `2`

Answer

C

Explanation

When a charged particle (charge `q , mass m`) enters perpendicularly in a magnetic field `(B)` than , radius of the path described by it `r = (mv)/(q^(B)) rArr mv = qBr`.
Also de - Broglie wavelength `lambda = (h)/(mv)`
`rArr lambda = (h)/( qBr) rArr (lambda_(alpha))/(lambda_(p)) = (q_(p) r_(p))/(q_(alpha) r_(alpha)) = (1)/(2)`