The rate of change of is 0.270 Bq per gram of carbon for the bones of a person who had just died.What is the decay constant? The half life of is 5.73 *10³ y^-1.

Question

Quizplus · Accepted Answer

We can use the following formula to relate the decay constant (lambda) and the half-life (t1/2):

lambda = ln(2)/t1/2

Substituting t1/2 = 5.73x10^10 seconds = 1.81x10^3 years, we get:

lambda = ln(2)/(1.81x10^3) years^-1
lambda = 3.83x10^-4 years^-1

To convert the given rate of change (0.270 Bq/g of carbon) to lambda, we need to use the following formula:

lambda = (ln(N(t)/N0)) / (-t)

where N0 is the initial number of radioactive nuclei, N(t) is the number of radioactive nuclei at time t, and t is the elapsed time.

Here, we can assume that N0 = N(t) (since the person has just died and no radioactive decay has occurred yet), so we can simplify the formula to:

lambda = (ln(1)) / (-t) = 0

This means that the given rate of change (0.270 Bq/g of carbon) is not consistent with any non-zero value of lambda. However, we can calculate the rate of change that corresponds to the calculated value of lambda:

dN/dt = -lambda*N
dN/dt = -3.83x10^-4 * N    (since N(t) = N0 = 1 for a freshly dead person)
dN/N = -3.83x10^-4 * dt
ln(N(t)/N0) = -3.83x10^-4 * t
ln(1) = -3.83x10^-4 * (1 g of carbon)
t = 1 / (0.270 Bq/g of carbon * 3600 s/h)
t = 1.34x10^6 s

This means that the activity of the bones would decrease to half its initial value after a time period equal to the half-life, as expected. Therefore, the only answer choice that is consistent with the given information is A, 1.21x10^-4 years^-1.

The Rate of Change of Is 0