A-LevelPhysicsParticle physics9702/41 · May/June 2020 · Q116 Marks

An electron, at rest, has mass mₑ and charge –q. A positron is a particle that, at rest, has mass mₑ and charge +q. A positron interacts with an electron. The electron and the positron may be considered to be at rest. The outcome of this interaction is that the electron and the positron become two gamma-ray (γ-ray) photons, each having the same energy. (a) Calculate, for one of the γ-ray photons:

(a)(i)the photon energy, in J[2]
(a)(ii)its momentum.[2]
(b)State and explain the direction, relative to each other, in which the γ-ray photons are emitted.[2]

Mark scheme

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

[C1] E = mc²
[A1] = 9.11 × 10⁻³¹ × (3.0 × 10⁸)² = 8.2 x 10⁻¹⁴ J
[C1] p = h/λ and E = hc/λ or E = pc
[A1] p = (8.2 × 10⁻¹⁴) / (3.0 × 10⁸) = 2.7 x 10⁻²² N s
[B1] total momentum (before and after interaction) is zero / momentum must be conserved (in the interaction) / momentum of the photons must be equal and opposite
[B1] (photons emitted in) opposite directions

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