An electron beam accelerated from rest through a potential difference of 5000 V in vacuum is allowed to impinge on a surface normally. The incident current is 50`muA` and if the electrons come to rest on striking the surface the force on it is

Options

A. `1.1924xx10^-8N`
B. `2.1xx10^-8N`
C. `1.6xx10^-8N`
D. `1.6xx10^-6N`

Answer

A

Explanation

Energy `=(1)/(2)mv^2=5000eV`
`=5000xx1.6xx10^-19J`
`mv=sqrt(2xx5000xx(1.6xx10^-19)m)`
`=4xx10^-8sqrtm`
Number of electrons striking per second is
`n=(q)/(e)=(It)/(e)=(50xx10^-6xx1)/(1.6xx10^-19)=31.25xx10^13`
Force=change of momentum per second
`=n(mv)=31.25xx10^13xx4xx10^-8sqrtm`
`=125xx10^5sqrt(9.1xx10^-31)`
`=1.1924xx10^-8N`