An isotope of potassium K40 undergoes two parallel type of decay, one by electron capture and other by β decay with half lives as 1.3 × 109 years and \frac{1 .3}{9} \times \left(10\right)^{9} years respectively. If in a sample of a mineral mass ratio of K : Ar : Ca is 5, 1.5 & 16 then calculate age of the mineral if it is known that all Ca40 in the mineral is not from the radioactive decay of potassium. [Express your answer in terms of 107 years for eg. if you answer is 2 × 109 years fill 0200]

Engineering

Chemistry

Application of Radioactivity

Question

An isotope of potassium K⁴⁰ undergoes two parallel type of decay, one by electron capture and other by β decay with half lives as 1.3 × 10⁹ years and $\frac{1 .3}{9} \times 10^{9}$ years respectively. If in a sample of a mineral mass ratio of K : Ar : Ca is 5, 1.5 & 16 then calculate age of the mineral if it is known that all Ca⁴⁰ in the mineral is not from the radioactive decay of potassium.
[Express your answer in terms of 10⁷ years for eg. if you answer is 2 × 10⁹ years fill 0200]

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Assumed that all Ar produced from K.
K Ar Ca
t = 0 a 0 0
t = t a–x–y x y produced
$\frac{x}{y} = \frac{λ_{1}}{λ_{2}} = \frac{{(t_{1 / 2})}_{2}}{{(t_{1 / 2})}_{1}} = \frac{1}{9}$
y = 9 x
x = $\frac{1 .5}{40}$ y = $\frac{9 \times 1 .5}{40}$
a–x–y = $\frac{5}{40}$
a = $\frac{5}{40} + \frac{1 .5}{40} + \frac{9 \times 1 .5}{40} = \frac{20}{40}$
lt = ln $\frac{a}{a - x - y}$
$(\frac{\ln 2}{1 .3 \times 10^{9}} + \frac{\ln 2}{\frac{1 .3}{9} \times 10^{9}}) t = \ln \frac{20 / 40}{5 / 40}$
t = 26 × 10⁷

Please subscribe our Youtube channel to unlock this solution.