Charge Is Conserved — Question 9

Question 9

Ionization and electron loss have different effects on gas charge

An initially neutral gas creates 1200 singly positive ion–electron pairs per second. Recombination removes 400 such pairs per second. Additionally, 600 electrons per second escape to an initially neutral collecting wall; no ions escape. Rates are constant for one second and the supplied counts are feasible throughout that interval.

1. Find the ion and free-electron populations added to the gas during the second and its final net charge.

2. Find the wall charge and the combined total. Write a general balance showing why pair creation and recombination cancel out of the gas net-charge rate.

Question 9 - Solution

Ionization and electron loss have different effects on gas charge

(a) Method and calculation

$$\Delta N_i=1200-400=800,\quad\Delta N_e=1200-400-600=200.$$$$\Delta Q_{\mathrm{gas}}=e(800-200)=+600e,\quad\Delta Q_{\mathrm{wall}}=-600e.$$

(b) Interpretation and further calculation

$$\dot Q_{\mathrm{gas}}=e[(G-R)-(G-R-L)]=eL.$$$$\Delta(Q_{\mathrm{gas}}+Q_{\mathrm{wall}})=0.$$Generating or recombining a positive ion and an electron changes charged-particle counts without changing net charge. Selective electron escape changes the gas subsystem charge.

Physical check

The wall must be included when testing conservation for the complete gas-and-collector system.