Asample of argon-39 had an original mass of 1578 grams. after 538 years, the sample is 394.5 grams. what is the half-life of argon-39? a. 135 years b. 180 years c. 269 years d. 538 years

C. 269 years

Explanation:

First, we have to find the value of the rate constant (k) through the following expression.

where,

is the amount of Ar at a certain time t

is the initial amount of Ar

Provided the rate constant, we can find the half-life (t1/2).

t1/2 = ln 2/k = ln 2/2.577 × 10⁻³ y⁻¹ = 269.0 y

the answer is 75.0%.