The questions are on the nuclear decay test. Take it under real conditions before reading the mark scheme.
Quick answer: Atoms have discrete energy levels, so they emit and absorb photons of fixed energy equal to the gap between levels. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 2 test on nuclear decay, from hydrogen transition to fusion and fission, with the equivalent answers to accept.
Marks are shown for each step. Method marks are given for a correct relationship even if the arithmetic slips, but final answers need units.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 15
Question 1 Hydrogen transition (3 marks)
a. ΔE = −1.51 − (−13.6) = 12.1 eV.b. λ = 1240 / 12.1 = 102.5 nm, about 103 nm.
c. Ultraviolet.
Marking: one mark each part.
Question 2 Absorption (2 marks)
a. Also, the 10.2 eV photon.b. Moreover, it matches the gap between n = 1 and n = 2 exactly (−3.40 − (−13.6) = 10.2 eV). The 10.0 eV photon matches no gap and so passes through.
Marking: correct photon (1); matching reason (1).
Question 3 Alpha decay (2 marks)
a. ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He.b. mass number (210 = 206 + 4) and charge or atomic number (84 = 82 + 2) are conserved.
Marking: balanced equation (1); both quantities (1).
Question 4 Beta decay (2 marks)
a. Xenon-131: A = 131, Z = 54.b. A neutron turns into a proton, and an electron and an antineutrino are emitted.
Marking: one mark each part.
Question 5 Half-life calculation (3 marks)
a. 36 h is 3 half-lives: 40 → 20 → 10 → 5.0 mg.b. 40 → 2.5 mg needs 4 half-lives, so 48 h.
Marking: number of half-lives (1); mass (1); time (1).
Question 6 Decay graph (3 marks)
a. 800 falls to 400 in 6 hours, so T = 6 h.b. Also, at 18 hours the rate is 100 per minute.
c. Each half-life removes only half of what is left, so some nuclei always remain.
Marking: one mark each part.
Question 7 Mass defect (3 marks)
a. E = 0.0150 × 931.5 = 14.0 MeV.b. 13.97 × 1.60 × 10⁻¹³ = 2.24 × 10⁻¹² J.
c. E = Δm c²: lost mass appears as released energy.
Marking: one mark each part.
Question 8 Fusion and fission (2 marks)
a. Light nuclei have low binding energy per nucleon; fusing moves them up the curve to a more tightly bound nucleus and the extra binding energy is released.b. Very heavy nuclei sit below the peak; splitting gives middle-sized nuclei that are more tightly bound per nucleon, so energy is released.
Marking: one mark each part.
