Here are activity data tables for five different radioactive isotope samples. De

Question

Here are activity data tables for five different radioactive isotope samples. Decay rates were measured at regular time intervals as listed. Each data entry is the number of decays measured during a one minute time interval. Write a lab report that analyzes these data to determine (1) the half-life of each of the samples, (2) the activity at the outset, (3) the number of radioactive nuclei present at the outset. In addition to the data tables, please include graphs that show the decay rates as a function of time. Plot curves to fit the data on the graphs. Provide summary tables of the results.

Explanation / Answer

The activity of a radiactive sample at any instant t is defined as the number of disintegrations occuring in the sample in unit time.

The activity at outset refers to the activity at t=0.

Now, the radioactive decay law is: Nt = N0e-kt, where k is the decay constant.

Differentiating the above eqn w.r.t. time, we get: dNt / dt = -kN0 e-kt              ..........(i)

At t=0, (dNt / dt)0 = -kN0                                            ( The -ve sign indicates that activity decreases with time)

Thus, At = A0 e-kt                                                                                      .........(ii)

Since the second question is being asked, assuming that the first one has been solved, the activity at outset can be calculated as follows:

k=0.693/T.

Calculate A0 from the decay law by substituting the values from the data record at any time into equation (ii).

This will give you the offset. Do this for each sample to calculate the activity at outset.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.