Answer:
C. 269 years
Explanation:
First, we have to find the value of the rate constant (k) through the following expression.
[tex][Ar]_{t}=[Ar]_{0}.e^{-k.t}[/tex]
where,
[tex][Ar]_{t}[/tex] is the amount of Ar at a certain time t
[tex][Ar]_{0}[/tex] is the initial amount of Ar
[tex]394.5g=1578g.e^{-k.538y} \\k = 2.577 \times 10^{-3} y^{-1}[/tex]
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
