The gas between the capacitor plates separated by a distance d is uniformly ionized by ultraviolet radiation so that n0 electrons per unit volume per second are formed. A constant potential difference is applied across the capacitor. These electrons moving in the electric field of the capacitor ionize gas molecules each electron producing α new electrons per unit length of its path. Ionization by ions is neglected. Plate 1 is at higher potential compared to plate 2. Which of the following are correct?
(Neglect mutual interaction between electrons)
A) The number of electrons per unit volume at a distance of x from plate 2 is n0eαx
B) The number of electrons per unit volume at a distance of x from plate 2 is n0(1+αx)
C) The electronic current density at plate 1 is en0deαd
D) The electronic current density at plate 1 is αen0(eαd−1)