Charge Is Quantized — Question 10

Question 10

Pair-only transfer preserves charge parity without changing the elementary unit

An ideal device allows an island to exchange electrons only in pairs. Its initial charge is $-3e$. Removing one electron pair increases island charge by $2e$; adding one pair decreases it by $2e$. Assume ordinary integer charge states but no allowed single-electron transfer in this device.

1. Write the set of reachable island charges and determine whether the island can become neutral.

2. Find the reachable charge states closest to zero and the minimum number of pair-removal events from the initial state to reach each. Explain why a measured step size $2e$ does not imply that electrons carry charge $-2e$.

Question 10 - Solution

Pair-only transfer preserves charge parity without changing the elementary unit

(a) Method and calculation

$$Q_m=(-3+2m)e,\qquad m\in\mathbb Z.$$$$Q_m=0\Rightarrow m=3/2\notin\mathbb Z:\quad\text{neutrality is unreachable}.$$

(b) Interpretation and further calculation

$$Q/e=-1:\ m=1;\qquad Q/e=+1:\ m=2.$$$$\min_m|Q_m|=e,\quad\Delta Q=\pm2e.$$The allowed process preserves odd charge parity. The observed jump combines two ordinary electrons; it describes a transfer restriction, not a new elementary particle charge.

Physical check

One additional allowed single-electron event would break this parity restriction while preserving charge quantization.