Strontium-90 undergoes radioactive decay according to the nuclear equation
3890Sr⟶3990Y+e−+νˉe.
Environmental scientists collected the activity data shown below for a sealed soil sample initially containing 1.00×106 Bq of 90Sr. The activity is directly proportional to the number of undecayed nuclei.
Time, t (yr) Activity, At (Bq)
0 1.00×106
10.0 8.17×105
20.0 6.68×105
30.0 5.46×105
40.0 4.46×105
(1) Show how the data can be linearized so that a straight-line plot versus time is obtained. Provide the transformed numerical values that would appear on the plot.
(2) From your transformed data, determine the numerical value of the decay constant for 90Sr in yr⁻¹, including the method you used to extract the value.
(3) Calculate the experimental half-life of 90Sr from the decay constant you obtained and compare it with the literature value of 28.8 yr. Comment on the degree of agreement in light of possible experimental uncertainties.
(4) Assuming the decay follows the same kinetics, estimate how many years are required for the activity of the sample to fall below 1.00×105 Bq. Show all calculations and state any assumptions clearly.