What is the de Broglie wave lenght of an electron, which is accelerated from the rest, through a potential difference of 100 V?

Explanation

Potentail difference = `V = 100 V`
Potential energy = `eV = 1.609 xx 10^(-19)C xx 100`
`1/2 mV^2 = 1.609 xx 10^(-17) J`
`V^2 = (2 xx 1.609 xx 10^(-17))/(m)`
m = mass of electron = `9.1 xx 10^(-31) Kg`
`:. V^2 = (2 xx 1.609 xx 10^(-17))/(9.1 xx 10^(-31))`
`:. V = sqrt((2 xx 1.609 xx 10^(-17))/(9.1 xx 10^(-31)))`
`= sqrt((2 xx 1.609 xx 10^(-17) xx 10^(31))/(9.1))`
`V = sqrt((3.218 xx 10^14)/(9.1))`
`V = 5.93 xx 10^(6) m//s`
`lambda = h/(mv)`
= where`lambda = 6.62 xx 10^(-34) Js`
`= (6.62 xx 10^(34))/(9.1 xx 10^(-31) xx 5.93 xx 10^6)`
`= 1.2 xx 10^(-10) m`
`lambda = 1.2 Å`.