What is the de-Broglie wavelength associated with (a) an electron moving with speed of `5.4xx10^6ms^-1`, and (b) a ball of mass 150g traveling at `30.0ms^-1`? `h=6.63xx10^(-34)Js`, mass of electron `=9.11xx10^(-31)kg`.

Explanation

(a) For the electron:
Mass m =`9.11xx10^(-31) kg` , speed `v=5.4xx10^(6)` m/s . Then, momentum p = mv =`9.11xx10^(-31)` kg x `5.4xx10^(6)`(m/s)
`p=4.92xx10^(-24)` kg m/s
de Broglie wavelength , `lambda`=h/p
`=(6.63xx10^(-34) Js)/(4.92xx10^(-24) Kg m//s)`
`lambda=0.135 nm`
(b) For the ball:
Mass m' =`0.150 kg` , speed `v'=30.0` m/s . Then, momentum p' = m'v' =0.150 (kg )x30.0 (m/s)
`p'=4.50` kg m/s
de Broglie wavelength , `lambda'`=h/p'
`=(6.63xx10^(-34) Js)/(4.50xx Kg m//s)`
`lambda'=1.47xx10^(pm34) nm`
The de Broglie wavelength of electron is comparable with X-ray wavelengths. However, for the ball it is about `10^(–19)` times the size ofthe proton, quite beyond experimental measurement