A nuclide of the isotope potassium-40 \(\left( {{}_{19}^{40}{\rm{K}}} \right)\) decays into a stable nuclide of the isotope
argon-40 \(\left( {{}_{18}^{40}{\rm{Ar}}} \right)\). Identify the particles X and Y in the nuclear equation below.

\[{}_{19}^{40}{\rm{K}} \to {}_{18}^{40}{\rm{Ar + X + Y}}\]

The half-life of potassium-40 is 1.3×10⁹yr. In a particular rock sample it is found that 85 % of the original potassium-40 nuclei have decayed. Determine the age of the rock.

State the quantities that need to be measured in order to determine the half-life of a long-lived isotope such as potassium-40.

neutrino/ν;
positron / e⁺ / \({}_{ + 1}^0{\rm{e}}\) / β⁺;
Award [1 max] for wrongly stating electron and antineutrino. Both needed for the ECF.
Order of answers is not important.

\(\lambda  = \left( {\frac{{\ln 2}}{{1.3 \times {{10}^9}}} = } \right)5.31 \times {10^{ - 10}}{\rm{y}}{{\rm{r}}^{ - 1}}\);
\(0.15 = {{\rm{e}}^{\left[ { - 5.31 \times {{10}^{ - 10}} \times t} \right]}}\);
t=3.6×10⁹yr;
Award [3] for a bald correct answer.

or

(0.5)ⁿ=0.15;
\(n = \frac{{\log \left( {0.15} \right)}}{{\log \left( {0.5} \right)}} = 2.74{\rm{half - lives}}\);
2.74×1.3×10⁹=3.6×10⁹yr;
Award [3] for a bald correct answer.

the count rate/activity of a sample;
the mass/number of atoms in the sample;