A metallic conductor carries current through a sea of free electrons drifting through a fixed lattice of positive metal ions. Resistance measures how much this drift is impeded, and the impediment comes mainly from electrons scattering off the lattice.

When the temperature rises, the following mechanism operates:

• The extra thermal energy is absorbed by the lattice ions, which vibrate about their mean positions with larger amplitude and higher frequency.
• These vibrating ions present a larger effective obstruction to the moving electrons, so an electron travels a shorter average distance (a smaller mean free path) before it is scattered.
• More frequent and more energetic collisions randomise the electron motion more often, reducing the net drift and therefore increasing resistance.

Quantitatively this is captured by R = R₀(1 + α·ΔT), where α, the temperature coefficient of resistance, is positive for metals. Because the collision picture is really about lattice vibrations, the choice describing more frequent atomic collisions inside the conductor is the correct underlying reason.

The other choices fail on physical grounds. Saying atomic vibrations decrease is the opposite of what heating does — vibrations grow, not shrink. Claiming the number of free electrons becomes zero is wrong because in a metal the free-electron concentration is essentially fixed and does not vanish with modest heating (this idea actually describes semiconductors in reverse — there carriers increase with temperature and resistance falls). The notion that the conducting path becomes physically shorter is meaningless, since the geometry of the wire does not shrink; if anything, thermal expansion slightly lengthens it, and the dominant effect on resistance remains the increased scattering.