Question

Immediately after the Chernobyl nuclear accident, the concentratiorn of 137Cs (cesium 137) in cow's milk was 12,000 Bq/L (a Becquerel is a measure of radioactivity; one Becquerel equals one radioactive disintegration per second). Assume that the only reaction by which the 137Cs was lost from the soil was through radioactive decay. Also assume that the concentration in cows milk is directly proportional to the concentration in the soil. Calculate the concentration of 137Cs in cow's milk (from feeding on grass in the soil) 5 years after the accident given a half-life for 137Cs of 30 years.

Answer 1

Answer: The concentration of cow's milk after 5 years is 10691 Bq/L

Explanation:

All the radioactive reactions follow first order kinetics.

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

$t_{1/2}=\frac{0.693}{k}$

We are given:

$t_{1/2}=30yrs$

Putting values in above equation, we get:

$k=\frac{0.693}{30}=0.0231yr^{-1}$

The equation used to calculate time period follows:

$N=N_o\times e^{-k\times t}$

where,

$N_o$ = initial concentration of Cow's milk = 12000 Bq/L

N = Concentration of cow's milk after 5 years = ?

t = time = 5 years

k = rate constant = $0.0231yr^{-1}$

Putting values in above equation, we get:

$N=12000Bq/L\times e^{-(0.0231yr^{-1}\times 5yr)}\\\\N_o=10691Bq/L$

Hence, the concentration of cow's milk after 5 years is 10691 Bq/L