(c) distinction between conductors, semiconductors and insulators in terms…

The idea

The three classes of material are distinguished by the number density n of charge carriers available to move. In a conductor such as copper, each atom contributes roughly one free electron, so n is very large, of order 10²⁸ to 10²⁹ m⁻³, and a small drift velocity gives a large current. In an insulator such as polythene, almost all electrons are bound to atoms, so n is extremely small and negligible current flows. A semiconductor such as silicon has a much smaller n than a metal, typically 10¹⁶ to 10¹⁹ m⁻³ at room temperature, but n rises steeply with temperature as more electrons are freed, so its resistance falls. Since I = Anev, at a fixed current a smaller n requires a larger drift velocity.

What earns the marks

• States that conductors have a very high number density of charge carriers, insulators a very low one, and semiconductors an intermediate value.
• Links the size of n to the current produced for a given drift velocity through I = Anev.
• Explains that in semiconductors n increases with temperature, so resistance decreases.
• Recognises that in metals n is approximately constant with temperature, while lattice vibrations dominate resistance.
• Uses order-of-magnitude values, for example n ≈ 10²⁸ m⁻³ for copper and n ≈ 10¹⁶ m⁻³ for intrinsic silicon.

Common mistakes and how to put them right

• Saying insulators have no charge carriers at all.

  Put it right: They have very few mobile carriers, which is why the current is negligible rather than exactly zero.

• Confusing number density n with resistivity or resistance.

  Put it right: n is a property of the material's carrier population, not a direct measure of opposition to current.

• Claiming n in a metal increases greatly with temperature.

  Put it right: In a metal n is roughly constant and the resistance rise comes mainly from increased lattice vibration.

• Assuming a semiconductor behaves like a metal because both conduct.

  Put it right: A semiconductor's conductivity depends strongly on temperature and on doping.

Exam tips

• Quote approximate orders of magnitude for n to support your comparison.
• Link every statement about n back to I = Anev so the physics reasoning is explicit.
• For temperature questions, separate the effect on n from the effect on lattice vibrations.
• Use the phrase 'number density of charge carriers' rather than 'number of electrons' to stay precise.