Question

Lead-209, a radioactive isotope, decays to nonradioactive lead over time. the half-life of lead-209 is 8 days. suppose that 20 milligrams of lead-209 are created by a particle physics experiment. write an equation for the amount of lead-209 present t days after the experiment

Answer 1

Radioactive elements undergoes first order decay. 

Now, for 1st order decay kinetics, rate constant (k) can be estimated as follows

k = 0.639/ t1/2,
where t 1/2 = half-life of radioactive material = 8 days (For Pb-209)

Also, we know that
$t = \frac{2.303}{k}log \frac{Co}{Ct}$  .................(1)

Here, Co = initial conc. of radioactive element
Ct = conc. of radioactive element at time t
t = time required to reach the concentration Ct


Thus, equation 1 can be used to estimate the amount of lead-209 present after 't' days.