An ionization chamber with parallel conducting plates as anode and cathode has `5 xx 10^(7)` electrons and the same number of singly-charged positive ions per `cm^(3)`. The electrons are moving towards the anode with velocity `0.4 m//s`. The current density from anode to cathode is `4 mu A//m^(2)`. The velocity of positive ions moving towards cathode is

Options

A. `0.4 m//s`
B. `16 m//s`
C. Zero
D. `0.1 m//s`

Answer

D

Explanation

(d) Current density of drifting electron `j = n e v`
`n = 5 xx 10^(7) cm^(-3) = 5 xx 10^(7) xx 10^(6) m^(-3)`
`v = 0.4 ms^(-1), e = 1.6 xx 10^(-19) C implies j = 3.2 xx 10^(-6) Am^(-2)`
Current desity of ions
`= (4 - 3.2) xx 10^(-6) = 0.8 xx 10^(-6) (A)/(m^(2))`
This gives `v` for ions `= 0.1 ms^(-1)`.