Question

Potassium-40 decays with a half-life of $1.3\times {10}^9$ yr. What is the age of lunar rock sample that contains these isotopes in the ratio 34.1 atoms ${}^{40}K:65.9$ atoms ${}^{40}Ar$? Assume that no argon was originally in the sample and that none has been lost by weathering.

• A. $1.236\times {10}^{9}years$
• B. $5.236\times {10}^{9}years$
• C. $2.226\times {10}^{9}years$
• D. None of these

Answer 1

The correct option is A $1.236\times {10}^{9}years$

(Ar) = 65.9 atoms $=N_0$
(K) = 39.1 atoms = N
$\therefore \lambda =\frac{2.303}{t}log\frac{N_0}{N}$
$\frac{0.693}{t_{50}}=\frac{2.303}{t}log\frac{N_0}{N}$
$\frac{0.693}{1.3\times 1069}=\frac{2.303}{t}log\frac{65.9}{34.1}$
$t=1.236\times {10}^{9}years$