Half-Life Analysis from Radioactive Decay Data
You are provided with data from a radioactive decay experiment. The data records the count rate, N, as a function of time, t. Use the following data: t (s): 0, 10, 20, 30, 40, 50 N (counts s⁻¹): 1000, 800, 640, 512, 410, 328 (a) Plot the graph of count rate versus time, labeling the […]
Calculating Radioactive Sample Activity
A sample of a radioactive isotope contains \(6.0 \times 10^{18}\) radioactive nuclei and has a decay constant of \(2.5 \times 10^{-4}\, \text{s}^{-1}\). Using the relationship \(A = \lambda N\), calculate the activity of the sample in becquerels (Bq). Express your answer in scientific notation to the appropriate number of significant figures.
Determining Radioactive Decay Parameters
A radioactive sample has an initial activity \(A_0\) of 8000 Bq. After a time \(t\) of 600 seconds, its activity \(A\) decreases to 2000 Bq. \n\na) Calculate the decay constant \(\lambda\) of the sample.\n\nb) Determine the half-life \(T_{1/2}\) of the sample.\n\nUse the value \(\ln2 \approx 0.693\).
Understanding the Decay Constant in Radioactive Decay
Which of the following best describes the physical meaning of the decay constant \(\lambda\) for a particular radioactive nuclide?
Part a
Using the decay model \(Q(t) = Q_0 e^{-kt}\) and the data \(Q(0)=100\) grams and \(Q(5)=80\) grams, set up the equation to determine the decay constant \(k\) and express the complete decay equation.
Part b
Using the decay constant \(k = -\\frac{\\ln(0.8)}{5}\) from part (a), determine the half-life \(T_{1/2}\) of the substance.