A proton and and `alpha `- particle are accelerated through a potential difference of `100 V`. The ratio of the wavelength associated with the proton to that associated with an `alpha` - particle is

Options

A. `sqrt(2) : 1`
B. `2 : 1`
C. `2 sqrt(2) : 1`
D. `(1)/( 2 sqrt(2)) : 1`

Answer

C

Explanation

`lambda = (h)/(sqrt(2 m QV)) rArr lambda prop (1)/(sqrt(mQ)) rArr (lambda_(p))/(lambda_(alpha)) = sqrt((m_(alpha) Q_(alpha))/( m_(p) Q_(p)))`
`rArr sqrt((4m_(p) xx 2 Q_(p))/( m_(p) xx Q_(p))) = 2 sqrt(2)`