Question

The air between two closely located plates is uniformly ionized by ultraviolet radiation. The air volume between the plates is equal to V = 500 cm3, the observed saturation current is equal to Isat = 0.48 μA. Find:

(a) the number of ion pairs produced in a unit volume per unit time;

(b) the equilibrium concentration of ion pairs if the recombination coefficient for air ions is equal to r = 1.67 x 10-6 cm3/*.

Answer 1

When the current is saturated, all the ions, produced, reach the plate.

Then,

(Both positive ions and negative ions are counted here)

The equation of balance is

The first term on the right is the production rate and the second term is the recombination rate which by the usual statistical arguments is proportional to n2 (= no of positive ions x no. of -ve ion). In equilibrium,

dn/dt = 0

So,