Answer:
Option C is correct.
t = 1.95 billion years.
Explanation:
Radioactive decay follows a first order reaction kinetics.
On solving the dynamic equation (the differential equation), this is obtained
C(t) = C₀ e⁻ᵏᵗ
C(t) = amount of radioactive material remaining after time t = 37.5%
C₀ = Initial amount of radioactive material = 100%
t = time that has passed = ?
k = decay constant.
For a first order reaction, the decay constant is related to the half life through the relation
k = (In 2)/T
T = half life = 1.38 billion years
k = (In 2)/1.38
k = 0.5023 per billion years.
C(t) = C₀ e⁻ᵏᵗ
0.375 = e⁻ᵏᵗ
e⁻ᵏᵗ = 0.375
In e⁻ᵏᵗ = In 0.375 = -0.981
-kt = -0.981
t = (0.981/0.5023) = 1.95 billion years.
Hope this Helps!!!
