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

Since, `I = "ne"Av_(d) rArr I/A = J = "ne"v_(d)`
`J to` Current density
`n = 5 xx 10^(7)//cm^(3) = 5 xx 10^(7) xx 10^(6) m^(3):v_(d) = 0.4 m//s`
`J = 3.2 xx 10^(-6) A//m^(2)`
Current density of ions-
`(4-3.2) xx 10^(-6) = 0.8 xx 10^(-6) A//m^(2)`
`rArr v_(d) = 0.1 m//s`