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=m v=9.11xx10^(-31)(kg)xx5.4xx10^(9)(m//s)`
`p=4.92xx10^(-24)kgm//s`
de Broglie wavelength, `lambda=h//p`
`=(6.63xx10^(-34)Js)/(4.92xx10^(-24)kgm//s)`
`lambda=0.135nm`
(b) For the ball :
Mass `m.=0.150 kg," speed v. "=30.0m//s`
Then momentum `..=m.v.=0.150(kg)xx30.0(m//s)`
`p.=4.50kg m//s`
de Broglie wavelength `lambda.=h//p.`
`=(6.63xx10^(-34)Js)/(4.50xxkgm//s)`
`lambda.=1.47xx10^(-34)m`
The de Broglie wavelength of electron is comparable with X-ray wavelengths. However, for the ball it is about `10^(-19)` times the size of the proton, quite beyond experimental measurement.