Q243 · Practice questionComplex unfamiliar5 marks
QUESTION 243 (5 marks)
The diagram shows an electron and its antiparticle X annihilating to produce two photons. In the centre-of-momentum frame the initial total energy is and the initial total momentum is zero. Use , and .
a)[2 marks]
Identify X and state its electric charge and lepton number.
b)[2 marks]
Calculate the wavelength of each photon.
c)[1 mark]
Explain why the photons must travel in opposite directions in this frame.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) A positron, with charge and lepton number . (b) . (c) Their equal momenta must cancel to keep the total momentum zero.
Worked solution
(a) X is the electron's antiparticle, a positron. It has opposite electric charge and lepton number to an electron, so the incoming totals are and , matching photons.
(b) Zero total momentum and two massless final particles require equal, opposite photon momenta and hence equal energies. Each has . Therefore .
(c) Momentum conservation requires . With only two photons, their nonzero momentum vectors must be equal in magnitude and opposite in direction. The interaction diagram is not a scale drawing of photon trajectories.
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Identify X as a positron with charge .
Part a: State its lepton number .
Part b: Use the symmetric two-photon final state to determine each energy in joules.
Part b: Calculate each wavelength from photon energy.
Part c: Relate the opposite photon directions to zero total momentum.
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