An isotope of potassium $^{40}_{19}K$ is used to date rocks - AQA - A-Level Physics - Question 1 - 2017 - Paper 1

The weak interaction is the fundamental force responsible for the decay process of $^{40}K$ to $^{40}Ar$. This interaction is crucial as it facilitates transitions between different types of quarks in the particles involved, particularly during electron capture.

The energy of the emitted gamma photon can be calculated using the relation: E = rac{hc}{\lambda} Given energy $E = 1.46 \text{ MeV} = 1.46 \times 1.6 \times 10^{-13} \text{ J}$, where $h = 6.626 \times 10^{-34} \text{ J s}$ and $c = 3.00 \times 10^8 \text{ m/s}$, we solve for wavelength $\lambda$: $\lambda = \frac{hc}{E}$ Substituting the known values: $\lambda \approx 8.52 \times 10^{-13} \text{ m}$

To confirm the decay process, one could measure the emitted particles and photons.

If the decay is via electron capture, one would detect an emitted electron and an antineutrino.

Alternatively, if the decay is to form a $^{40}Ca$ nuclide, one would expect emissions typical of beta decay, where beta particles are emitted alongside neutrinos. The characteristics of these emissions can distinguish between the decay processes.