An `alpha`-particle and a proton are fired through the same magnetic field which is perpendicular to their velocity vectors. The `alpha`-partcles and the proton move such that radius of curvature of their paths is same. Find the ratio of their de Broglie wavelengths.

Options

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

Answer

A

Explanation

radius of curvature in magnetic field
`r = (mV)/(qB) " " ….(1)`
and `lambda = (h)/(mV) " " …..(2)`
`therefore` From (1) & (2)
`(lambda_(a))/(lambda_(p)) = (q_(p) r_(p))/(q_(alpha)r_(alpha)) = (1)/(2)`