A-LevelPhysicsQuantum physics9702/42 · May/June 2017 · Q119 Marks

An electron has charge –q and mass m. It is accelerated from rest in a vacuum through a potential difference V.

(a)Show that the momentum p of the accelerated electron is given by p = √(2mqV).[2]
(b)(i)State what is meant by the de Broglie wavelength.[2]
(b)(ii)Calculate the de Broglie wavelength of the electron. wavelength = ............................................................. m [3][3]
(c)The separation of copper atoms in a copper crystal is approximately 2 × 10⁻¹⁰ m. By reference to your answer in (b)(ii), suggest whether electron diffraction could be observed using a beam of electrons that have been accelerated through a potential difference of 120 V and are then incident on a thin copper crystal.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B1] loss of (electric) potential energy = gain in kinetic energy or qV = ½ mv² or Ek = p²/2m = qV
[B1] p = mv with algebra leading to p = √(2mqV)
[B1] particle/electron has a wavelength (associated with it)
[B1] dependent on its momentum or when/because particle is moving
[C1] p = (2 × 9.11 × 10⁻³¹ × 1.60 × 10⁻¹⁹ × 120)¹/²
[C1] λ = (6.63 × 10⁻³⁴) / (5.91 × 10⁻²⁴)
[A1] = 1.12 x 10⁻¹⁰ m
[M1] wavelength is similar to separation of atoms
[A1] so diffraction observed

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