Potassium-40 decays to argon-40 with a half-life of 1.27 × 109 yr. The age of a mineral sample that has a mass ratio of 40ar to 40k of 0.812 is yr.

The age of the mineral sample is

Explanation:

The equation used to calculate rate constant from given half life for first order kinetics:

where,

= half life of the reaction =

Putting values in above equation, we get:

We are given:

Mass ratio of K-40 to Ar-40 = 0.812 : 1.00

Rate law expression for first order kinetics is given by the equation:

where,

k = rate constant =

t = time taken for decay process = ? yr

= initial amount of the sample = [1.00 + 0.812] = 1.812 grams

[A] = amount left after decay process = 1.00 grams

Putting values in above equation, we get:

Hence, the age of the mineral sample is

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