The air between two closely located plates is uniformly ionized by ulraviolet radiation. The air volume between the plates is equal to `V = 500 cm^(3)`, the observed saturation current is equal to `I_(sat) = 0.48 muA`. Find:
(a) the number of ion pairs produced in unit voume per unit time,
(b) the equilibriium concentration of ion paris if tghe recombination coefficient for air lions is eaual to `r = 1.67.10^(-8) cm^(3)//s`

Explanation

When the current is satured, all the ions,produced, reach the plate.
Then, `dotn_(i) = (I_(sat))/(eV) = 6xx10^(9) cm^(-5) s^(-1)`
(Both positive ions and negative ions are counted here)
The equaction of balance is, `(dn)/(dt) = dotn_(i) - r n^(2)`
The first term on the right is the production rate and the secound term is the recombination rate which by the usual statistical arguments is proportional to `n^(2)` (= no of positive ions `xx` no of `-ve` ion). In equilibrium,
`(dn)/(dt) = 0`
so,`n_(eq) = sqrt((dotn_(i))/(r)) = 6xx10^(7) cm^(-5)`.