Metal resistance increases with temperature because of lattice vibrations

Resistivity & Superconductivity — AQA A-Level Physics

In a metal, the chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). carriers are conduction electronsDelocalised electrons in a metal that are free to move through the lattice structure and carry electric currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. (delocalised electrons).
The metal ions form a regular lattice and vibrate about fixed positions.
At higher temperatures, the ions vibrate with greater amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)..
Conduction electronsDelocalised electrons in a metal that are free to move through the lattice structure and carry electric currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. collide more frequently with the vibrating ions.
More collisions per second means greater opposition to currentThe rate of flow of charge. Measured in amperes (A).: higher resistanceThe opposition to current flow. The ratio of potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). to current. Measured in ohms (Ω)..
The number of charge carriers in a metal stays approximately constant with temperature.
The mechanism is entirely about increased collision frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz)., not about fewer electrons.

Two side-by-side diagrams of a metal lattice. Left (low temperature): small ion vibrations, electron path is relatively straight. Right (high temperature): large ion vibrations, electron path has many collisions.

Examiner Tips and Tricks

When explaining why metal resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). increases with temperature, the key phrase is 'ions vibrate with greater amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)., causing more frequent collisions with conduction electronsDelocalised electrons in a metal that are free to move through the lattice structure and carry electric current.'.
Do not say 'the electrons move faster' -- the applied current drives the drift velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.The average velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. of charge carriers through a conductor in the direction of current flow, typically very slow (~1 mm/s)., not thermal energyThe capacity to do work. Measured in joules (J)..