Answer:
1.56 x 10^4 years
Explanation:
Half life, T = 3400 years
initial amount, No = 24 g
Amount remaining, N = 1 g
Let λ be the decay constant.
λ = 0.6931 / T = 0.6931 / 3400 = 2.039 x 10^-4 per year
Let the 1 g amount is remaining in time t.
[tex]N = N_{0}e^{-\lambda t}[/tex]
[tex]1 = 24e^{-2.039\times 10^{-4}\times t}[/tex]
[tex]24= e^{2.039\times 10^{-4}\times t}[/tex]
Take log on natural base on both the sides
[tex]3.178= 2.039\times 10^{-4}\times t[/tex]
t = 1.56 x 10^4 years
