Find the de Broglie wavelength associated with a proton accelerated from rest through a potential difference of 5000 V. `[m_(p) = 1.673 xx 10^(-27) kg]`

Explanation

Data: `m_(p)= 1.673 xx 10^(-27) kg, h=6.63 xx 10^(-34) J.s,`
`KE=5000 eV = 5000 xx 1.6 xx 10^(-19) J = 8 xx 10^(-16)` J
`KE = 1/2mv^(2) = (m^(2)v^(2))/(2m) = p^(2)/(2m)`
`therefore p=sqrt(2m xx KE)`
`=sqrt(2 xx 1.673 xx 10^(-27) xx 8 xx 10^(-16))`
`=1.636 xx 10^(-21) kg.m//s`
The de Broglie wavelength, `lambda= h/p = (6.63 xx 10^(-34))/(1.636 xx 10^(-21))`
`=4.053 xx 10^(-13)` m