Question

Potassium-40 decays to argon-40 with a half- life of 1.27x 109 yrs. What is the age of a
rock in which the mass ratio of argon to potassium is 4.2?​

Answer 1

Answer:

$\frac{Undecayed}{total} = \frac{1}{2^n}$          where n= no. of half lives

$\frac{1}{5.2} = \frac{1}{2^n}$                     Ratio of potassium(undecayed) to argon(decayed)= 1:4.2

$2^n = 5.2$                     Ratio of undecayed mass(potassium) to total mass=1:5.2

$n log(2) = log(5.2)$

$n= 2.3785$

time of decay = n × half life

= 2.3785 × (1.27 x 10⁹)

= 3.02×10⁹ yrs