A-LevelPhysicsQuantum physics9702/42 · May/June 2020 · Q118 Marks

The uppermost energy bands in a solid are known as the valence band (VB), the forbidden band (FB) and the conduction band (CB). A copper wire is at room temperature. The structure of a copper crystal is to be examined using electron diffraction. Electrons, having been accelerated from rest through a potential difference V, are incident on the crystal. The de Broglie wavelength λ of the electrons is 2.6 × 10⁻¹¹ m.

(a)Use band theory to explain why the resistance of the copper wire increases as its temperature increases.[4]
(b)Calculate the accelerating potential difference V.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] conduction band and valence band overlap
[1] number (density) of charge carriers does not vary
[1] increase in temperature gives rise to increased lattice vibrations
[1] (lattice) vibrations hinder movement of charge carriers so resistance increases
[1] mv = h / λ
[1] v = (6.63 × 10⁻³⁴) / [(2.6 × 10⁻¹¹) × (9.11 × 10⁻³¹)]
[1] ( = 2.80 x 10⁷ m s⁻¹)
[1] qV = ½mv²
[1] V = [9.11 × 10⁻³¹ × (2.80 × 10⁷)²] / [2 × 1.60 × 10⁻¹⁹]
[1] = 2.2 × 10³ V

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