A sample of potassium-42 was measured to have the radioactivity shown in the table below. Based on the given data, what must the initial activity of the sample have been at zero hours?

Question

A sample of potassium-42 was measured to have the radioactivity shown in the table below.  Based on the given data, what must the initial activity of the sample have been at zero hours?

Quizplus · Accepted Answer

11ecba2d_1235_99e4_a3bf_1720d842ed01_MD0008_00 In radioactive decay, the half-life of a radioisotope is the time required for the amount of the isotope to decrease by half (50% of the initial amount). With each subsequent half-life interval that passes, the amount of the isotope that remains is again decreased by half so that the fraction of the initial amount remaining becomes exponentially smaller and eventually approaches zero. Accordingly, the fraction remaining after n half-lives can be calculated as: 11ecba2d_1235_c0f5_a3bf_a5319be09db4_MD0008_00 The activity of a radioisotope refers to the number of decay events per unit of time. In the International System of units (SI), the preferred unit of activity is the becquerel (Bq), in which 1 Bq equals 1 radioactive decay per second. Accordingly, radioisotope activity is proportional to the amount of the decaying radioisotope present, and activity decreases by 50% with each successive half-life that passes. 11ecba2d_1235_c0f6_a3bf_f50ddb796153_MD0008_00 11ecba2d_1235_c0f7_a3bf_991dc728fc34_MD0008_00 As shown in the data given in this question, the time required to decrease the amount of ⁴²K by 50% (the half-life) is 12 hours. This means that after 12 hours (one half-life, n = 1) the measured activity (1850 Bq in this case) is only half of the initial activity that was present at time zero. Therefore, the initial activity of the ⁴²K sample must have been two times higher. 11ecba2d_1235_c0f8_a3bf_87e9edfca94a_MD0008_00 11ecba2d_1235_c0f9_a3bf_e77a7ca2a81b_MD0008_00 (Choices A, B, and C) Based on a half-life of 12 hours, an initial activity greater than 3700 Bq would be too high to result in the measured activities in the table during the time intervals listed. Times prior to time zero would be negative and conceptually invalid. Educational objective: The activity of a radioisotope (the number of decay events per unit of time) is proportional to the amount of the decaying radioisotope present and decreases by 50% for each radioisotope half-life that passes. With each subsequent half-life, the initial amount of isotope that remains becomes exponentially smaller and eventually approaches zero.

A Sample of Potassium-42 Was Measured to Have the Radioactivity