Q194 · Practice questionComplex unfamiliar6 marks
QUESTION 194 (6 marks)
A photon produces an electron–positron pair in the field of a heavy nucleus. Use , and . The nucleus remains the same species and takes a small recoil energy.
a)[2 marks]
Calculate the minimum energy required for the two new rest masses, in MeV.
b)[2 marks]
Determine an upper bound on the pair's combined kinetic energy.
c)[2 marks]
Show that charge, baryon number and lepton number can all be conserved in this process.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
(a) (rest-mass budget before recoil). (b) ; actual combined kinetic energy is slightly less because of recoil. (c) The pair has , , ; the nucleus contributes unchanged totals.
Worked solution
(a) The pair's rest energy is . Dividing by gives . The exact nuclear-frame threshold is slightly higher because recoil must also be supplied.
(b) After supplying the rest masses, available energy is . This is an upper bound on pair kinetic energy: the nucleus also receives some recoil energy.
(c) The incoming photon has zero charge, baryon number and lepton number. For the pair, , and . The unchanged nucleus adds the same charge and baryon number to both sides.
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: Calculate the rest energy of two electron masses.
Part a: Convert to MeV and identify the rest-mass budget.
Part b: Subtract the rest-energy budget from photon energy.
Part b: Account for nuclear recoil in interpreting the bound.
Part c: Calculate the cancelling pair charge and lepton number and zero baryon number.
Part c: Include the unchanged nucleus when comparing initial and final totals.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusHow many marks did you earn?
Compare your working with the guide above.