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

The amount of lead-209 present after t days is determined by the equation N = 20(1/2)^(t/8), where N is the amount remaining, 20 is the initial amount in milligrams, and 8 is the half-life in days.

Step-by-step explanation:

The equation for the amount of lead-209 present t days after the experiment, given that lead-209 has a half-life of 8 days, can be derived from the concept of radioactive decay, which follows first-order kinetics. To calculate the amount of remaining lead-209 at any time t, we can use the half-life formula:

N = N_0 (1/2)^(t/t_{1/2})

Where N is the amount of the substance remaining after time t, N_0 is the original amount of the substance, t_{1/2} is the half-life of the substance, and t is the time elapsed. For this example, if we start with 20 milligrams of lead-209, the equation would be:

N = 20(1/2)^(t/8)

This equation allows us to determine how much lead-209 would be left after any number of days.

Answer 2

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 = (2.303)/(k)log (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.