Question

A proton and α-particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelength λ_p to that λ_α is _______.

Options

• `sqrt2 : 1`

• 2 : 1

• `sqrt6 : 1`

• `sqrt8 : 1`

Answer 1

A proton and α-particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelength λ_p to that λ_α is `underline(sqrt8 : 1)`.

Explanation:

As `lambda = "h"/(sqrt(2 "mqV"))`

`therefore lambda prop 1/sqrt"mq" therefore lambda_"p"/lambda_alpha = (sqrt("m"_alpha" q"_alpha))/(sqrt("m"_"p" "q"_"p"))`

`therefore lambda_"p"/lambda_alpha = sqrt((4"m"_"p" xx 2"e")/("m"_"p" xx "e")) = sqrt8`