Wave property of electron implies that they will show diffraction effected . Davisson and Germer demonstrated this by diffracting electron from crystals . The law governing the diffraction from a crystals is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructiely

Electron accelerated by potential `V` are diffracted from a crystal if `d = 1 Å and i = 30^(@), V` should be about `(h = 6.6 xx 10^(-34) Js, m_(e) = 9.1 xx 10^(-31) kg , e = 1.6 xx 10^(-19)C)`

Options

A. `1000V`
B. `2000V`
C. `50V`
D. `500V`

Explanation

Path difference between two electrons waves reflected from the two planes of the atoms in a crystal is `dsin (90^(@)-30^(@))+d sin(90^(@)-30^(@))`
`=2dcos 30^(@)`
For differaction of these two waves `2dcos30^(@)=lambda` or `lambda=2dcos 30^(@)=2xx10^(-10)xxsqrt(3)//2`
`=sqrt(3)xx10^(-10)Å`
De-broglie wavelength, `lambda=h/(mv)=h/(sqrt(2Vem))`
or `V=(h^(2))/(2emlambda^(2))`
`=((6.6xx10^(-34))^(2))/(2xx(1.6xx10^(-19))xx(9.1xx10^(-31))xx(3xx10^(-20))^(2))`
`~~50V`