Physics

Problem

A particle of mass

m

and charge

q

is accelerated from rest through a potential difference

V

. (a) Derive an expression for its de Broglie wavelength

\lambda

in terms of

m

q

V

and fundamental constants. (b) Using your result, find the numerical value of the ratio

\dfrac{\lambda_{p}}{\lambda_{\alpha}}

for a proton

(q=+e,\,m=m_{p})

and an alpha particle

(q=+2e,\,m=4m_{p})

accelerated through the same potential difference.