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
[tex] t = \frac{2.303}{k}log \frac{Co}{Ct} [/tex] .................(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.
