Question

${ }^{40} K$ isotope of potassium has a half life of $1.37 \times 10^{9}$ years and decays to an isotope of argon which is stable. In a particular sample of moon rock, the ratio of potassium atoms to argon atoms was found to be $1: 7$. The age of the rock, assuming that originally there was no argon present, is

• A. $4.11 \times 10^{9}$ year
• B. $2.74 \times 10^{9}$ year
• C. $5.48 \times 10^{9}$ year
• D. $1.37 \times 10^{9}$ year

Answer 1

Answer: (A)

$T _{1 / 2}=1.37 \times 10^{9}$ year
Ratio $-$ Potassium : Argon $=1: 7$
Amount of Potassium left $=\frac{1}{8}$
$\left(\frac{1}{2}\right)^{n}=\frac{1}{8}$
$\therefore n$ or number of half lives $=3$