understand that the charge on charge carriers is quantised

Electric Current

Electric current is the rate at which electric charge flows past a given point in a circuit. It is defined by the relation

$$ I = \frac{\Delta Q}{\Delta t} $$

where $I$ is the current (in amperes, A), $\Delta Q$ is the amount of charge that passes (in coulombs, C), and $\Delta t$ is the time interval (in seconds, s).

Charge Carriers

In conductive materials the charge is carried by particles known as charge carriers. The nature of these carriers depends on the material:

• Metals – free electrons
• Electrolytes – ions (positive cations and negative anions)
• Semiconductors – electrons and holes

Quantisation of Charge

All observed charge carriers carry charge in integer multiples of a fundamental unit, the elementary charge $e$:

$$ q = n\,e \qquad n = \pm1,\pm2,\pm3,\dots $$

The accepted value of the elementary charge is

$$ e = 1.602 \times 10^{-19}\ \text{C} $$

This quantisation means that charge cannot exist in arbitrary fractions; it is always an integer multiple of $e$.

Experimental Evidence

1. Millikan oil‑drop experiment – measured the charge on individual oil droplets and found that all measured charges were integer multiples of $e$.
2. Photoelectric effect – electrons are emitted from a metal surface with charge exactly equal to $-e$.
3. Charge conservation in chemical reactions – ions exchange whole numbers of elementary charges.

Typical Charge Carriers and Their Charges

Carrier	Symbol	Charge ($q$)	Typical Material
Electron	$e^{-}$	$-e$	Metals, semiconductors
Proton	$p^{+}$	$+e$	Atomic nuclei
Alpha particle	$\alpha^{2+}$	$+2e$	Radioactive decay
Sodium ion	$\text{Na}^{+}$	$+e$	Electrolytes
Chloride ion	$\text{Cl}^{-}$	$-e$	Electrolytes

Applying Quantised Charge to Current Calculations

When a current $I$ flows through a conductor, the number of charge carriers $N$ passing a cross‑section per second is given by

$$ N = \frac{I}{e} $$

For example, a current of $1\ \text{A}$ corresponds to

$$ N = \frac{1\ \text{C s}^{-1}}{1.602 \times 10^{-19}\ \text{C}} \approx 6.24 \times 10^{18}\ \text{carriers per second} $$

Key Points to Remember

• All observable electric charge is an integer multiple of the elementary charge $e$.
• The quantisation of charge is a fundamental principle underlying the definition of electric current.
• Experimental techniques such as the Millikan oil‑drop experiment provide direct evidence for charge quantisation.
• Knowing the charge on individual carriers allows conversion between macroscopic current and microscopic carrier flow.