Radioactive Decay · Paper 2 — Free Physics HL Practice Questions

A nuclear reactor monitoring system uses a cobalt-60 source to test the integrity of steel reactor vessels. Cobalt-60 ($^{60}_{27}\text{Co}$) decays via beta-minus emission to nickel-60 ($^{60}_{28}\text{Ni}$). A technician measures the activity of a sealed source to be $1.8 \times 10^{12}\,\text{Bq}$ on 1 January 2020.

A medical physics laboratory tests a sealed iodine-123 source for thyroid imaging. The source has an initial activity of $4.8 \times 10^{8}\,\text{Bq}$. Iodine-123 has a half-life of $13.2\,\text{hours}$. The source is considered safe for patient handling when its activity falls below $1.5 \times 10^{7}\,\text{Bq}$. Relevant equations: $A = A_0 e^{-\lambda t}$, $\lambda = \dfrac{\ln 2}{T_{1/2}}$, $\ln 2 \approx 0.693$

A nuclear reactor used for research produces technetium-99m, a medical tracer. The decay constant of technetium-99m is $3.22 \times 10^{-5}\,\text{s}^{-1}$. A sample is prepared for a hospital and must contain at least $2.0 \times 10^{12}$ undecayed nuclei at the time of injection. Preparation and transport take $6.0$ hours from the reactor to the hospital.

A medical physicist is calibrating a cobalt-60 ($^{60}_{27}\text{Co}$) source for use in cancer radiotherapy. The source has an initial activity of $1.2 \times 10^{15}\,\text{Bq}$ at the time of manufacture. Cobalt-60 decays by beta-minus emission to an excited state of nickel-60 ($^{60}_{28}\text{Ni}^*$), which then promptly emits two gamma photons of energies $1.17\,\text{MeV}$ and $1.33\,\text{MeV}$ to reach the ground state. The half-life of cobalt-60 is $5.27$ years.