Chemistry - Radioactivity Question with Solution | TestHub

${\mathrm{K}}^{40}$ decays into ${\mathrm{Ca}}^{40}$ and ${\mathrm{Ar}}^{40}$ simultaneously as

K⁴⁰ $\stackrel{t_{1/2}=1.5\times 10^{9}yr}{\to }$ Ca⁴⁰ + β⁻

K⁴⁰ $\stackrel{t_{1/2}=1.2\times 10^{10}yr}{\to }$ Ar⁴⁰ + β⁺

If the atomic concentration of Ar in a sample of rock is 10% that of potassium and the only source of Ar is the radioactive disintegration of potassium, the age of the rock sample (in 10⁹ years) is:

($\ln 1.1=0.09$, $\ln 1.3=0.26$, $\ln 1.9=0.63$, $\ln 2.0=0.70$)