An `alpha`-particle and a proton are accelerated from rest by the same potential, thenthe ratio of their de-Broglie wavelength is

Options

A. `sqrt2`
B. `1/(sqrt2)`
C. `2sqrt2`
D. 2

Answer

C

Explanation

`lambda = (h)/(sqrt(2qVm))`
`lambda_(alpha) =(h)/(sqrt(2 xx 2 xx V xx m_alpha)) implies lambda_(alpha) = (h)/(sqrt(2xx 2 xx V xx 4))`
`lambda_p = (h)/(sqrt(2xx 1 xx V xx m_p)) implies lambda_P = (h)/(sqrt(2 xx 1 xx V xx 1))`
`(lambda_P)/(lambda_(alpha)) = sqrt((16)/(2)) implies (lambda_p)/(lambda_(alpha)) = 2sqrt2`