A medical technician is working with the four samples of radionuclides listed in the table below. Initially, each sample contains 12.00μmol of the radionuclide.First, order the samples by decreasing initial radioactivity. Then calculate how long it will take for the amount of radionuclide in each sample to decrease to /132 of the initial amount.sample radionuclide initial radioactivity time for amount of radionuclide to decrease to 1/32 of initial amountsymbol half-lifeA 192 Ir 74.0days days77B 178 Ta 9.0minutes minutes73C 212 Pb 11.hours hours82D 188 W 69.0days days74
Question
A medical technician is working with the four samples of radionuclides listed in the table below. Initially, each sample contains 12.00μmol of the radionuclide.First, order the samples by decreasing initial radioactivity. Then calculate how long it will take for the amount of radionuclide in each sample to decrease to /132 of the initial amount.sample radionuclide initial radioactivity time for amount of radionuclide to decrease to 1/32 of initial amountsymbol half-lifeA 192 Ir 74.0days days77B 178 Ta 9.0minutes minutes73C 212 Pb 11.hours hours82D 188 W 69.0days days74
Solution
The initial radioactivity of a sample is directly proportional to the number of radioactive atoms present, so all four samples start with the same radioactivity.
The time it takes for the amount of radionuclide to decrease to 1/32 of the initial amount can be calculated using the formula for radioactive decay:
t = (half-life) * log2(N0/N)
where N0 is the initial amount and N is the final amount. In this case, N0/N = 32.
Let's calculate the time for each sample:
A) For 192Ir with a half-life of 74.0 days: t = 74.0 days * log2(32) = 185.0 days
B) For 178Ta with a half-life of 9.0 minutes: t = 9.0 minutes * log2(32) = 22.5 minutes
C) For 212Pb with a half-life of 11.0 hours: t = 11.0 hours * log2(32) = 27.5 hours
D) For 188W with a half-life of 69.0 days: t = 69.0 days * log2(32) = 172.5 days
So, the order of samples by decreasing initial radioactivity is the same as the order given, A, B, C, D. The time it takes for the amount of radionuclide in each sample to decrease to 1/32 of the initial amount is 185.0 days for A, 22.5 minutes for B, 27.5 hours for C, and 172.5 days for D.
Similar Questions
In each of the following questions, calculate theamount remaining from a 100 mg sample of thegiven radioisotope after the specified time.a 105Rh has a half-life of 35 h. Calculate themass remaining after 70 h.b 209Po has a half-life of 105 y. Calculate themass remaining after 420 y.c 219Rn has a half-life of 3.96 s. Calculate themass remaining after 39.6 s.
Tin-129 is radioactive and has a half life of 2.23 minutes. How much of a 3.80mg sample would be left after 7.86 minutes?Round your answer to 2 significant digits. Also, be sure your answer has a unit symbol.
Derive an expression that relates the half-life and the decay constant for a sample of aparticular radioactive nucleus. Calculate the half-life and decay constant for a radioactiveisotope sample if the initial number of radioactive atoms is 450 and this reduces to 63 after24.3 hours.
Iodine-131 is radioactive and has a half life of 8.04 days. How long would it take a sample to decay from 8.80mg to 5.40mg.Round your answer to 2 significant digits.
Calculate the half-lives of each of the followingradioisotopes.a It takes 180 days for 80 mg of iron-59 to decayto 5 mg.b It takes 2.1 × 10 12 years for 60 mg ofplatimum-190 to decay to 7.5 mg.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.