What is the de-Broglie wavelength associated with (a) an electrin moving with a speed of `5.4xx10^(6)m//s` and (b) a ball of mass 150 g travelling at 30.0 m/s?

Explanation

(a)Here ,for electron
Speed of electron v=`5.4xx10^(6)m//s`
Mass of electron m=`9.11xx10^(-31)kg`
`h=6.63xx10^(-34) Js`
Momentum of electron.
P=mv
`therefore p=9.11xx10^(-31)xx5.4xx10^(6)`
`therefore p=49.194xx10^(-25)`
`therefore p~~4.92xx10^(-24) kg m//s`
`implies` Now ,de Broglie wavelength,
`lambda=(h)/(p)`
`therefore lambda =(6.63xx10^(-34))/(4.92xx10^(-24))`
`therefore lambda=1.34756xx10^(-10)m`
`therefore lambda~~0.135` nm
(b) For ball,
speed v=30.0 m/s
mass m=0.150 kg
`h=6.63xx10^(-34) Js`
`therefore` Momentum of ball
P=mv
`therefore P=0.15xx3.0`
`therefore` P= 4.50 kg m/s
`therefore` de-Broglie wavelength,
`lambda=(h)/(P)`
`therefore lambda=(6.63xx10^(-34))/(4.50)`
`therefore lambda=1.4733^(@)xx10^(-34)m`
`therefore lambda~~1.47xx10^(-34)m`