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

For the electron :
Mass m = `9.11 xx 10^(-31) `kg
speed `v= 5.4 xx 10^(6)` m/s Then , momentum
`P = m v = 9.11 xx10^(-31)("kg") xx 5.4 xx 10^(6)` (m/s)
` P = 4.92 xx 10^(-24) ` kg m/s
de Brogile wavelength , ` lambda =` h/p
` = (6.63 xx 10^(-34)Js)/(4.92 xx 10^(-24)kg" m/s")`
` lambda = 0.135 ` nm
(b) For the ball :
Mass m ' = 0.150 kg , speed `v' = 30.0` m/s
p' = 4.50 kg m/s
de Broglie wavelength `lambda ' = h//p' `
` = ( 6.63 xx10^(pm34)Js)/(4.50 xx"kg m/s")`
` lambda ' = 1.47 xx 10^(-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 .