Question

A proton `(mass = 1.66 xx 10^(-27)kg)` is moving with kinetic energy `5 xx 10^(-27) J` calculate the de Broglie wavelength associated with it ? `(h = 6.6 xx 10^(-34)Js)`

Answer 1

KE of proton = `(1)/(2) mv^(2) = 5 xx 10^(-27) J = 5 xx 10^(-27) kg m^(2)s^(-2)`
`v^(2) = (2 xx 5 xx 10^(-27) kg m^(2)s^(-2))/(1.66 xx 10^(-27)) kg = 6.024 m^(2)s^(-2)`
`v = sqrt(6.02m^(2)s^(-2)) = 2.454 m s^(-1)`
`lambda = (h)/(mv) = (6.6 xx 10^(-34) Js)/(1.66 xx 10^(-27) kg xx 2.454 m s^(-1)) = 1.6202 xx 10^(-7)m`