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. `1.1924 xx 10^(-8) N`
B. `2.1 xx 10^(-8) N`
C. `1.6 xx 10^(-8)N`
D. `1.6 xx 10^(-6) N`

Answer

A

Explanation

Energy `=(1)/(2)mv^(2) = 5000eV`
`=5000 xx 1.6 xx 10^(-19)` joule
`mv = sqrt(2xx5000 xx (16 xx 10^(-19)m))`
`= 4 xx 10^(-8) xx sqrt(m)`
Number of electron striking per second
`=n = (q)/(e) = (It)/(e) = (50xx10^(-6)xx1)/(1.6 xx 10^(-19))`
`= 31.25 xx 10^(13)`
Force `=` change of momentum per second
`=n(mv) = 31.25 xx 10^(13) xx 4xx10^(-8) sqrt(m)`
`= 125 xx 10^(5) sqrt(9.1 xx 10^(-31))`
`= 1.1924 xx 10^(-8)` newton