If the decay constant for 131I is 9.98 x 10^-7 s-1, calculate the activity of a 1.00 mg sample.

Question

Quizplus · Accepted Answer

The activity of a radioactive sample is given by the formula A = λN, where λ is the decay constant and N is the number of radioactive atoms present in the sample. To calculate the number of radioactive atoms, we need to convert the mass of the sample to the number of atoms using Avogadro's number (6.022 x 10^23 atoms/mol).

First, we need to calculate the half-life of 131I using the formula t1/2 = ln(2)/λ. Substituting the given value of λ, we get t1/2 = 6.94 days.

Next, we can calculate the number of radioactive atoms present in 1.00 mg of 131I using its molar mass (130.91 g/mol) and Avogadro's number:

N = (1.00 mg / 130.91 g/mol) x (6.022 x 10^23 atoms/mol) = 4.59 x 10^14 atoms

Finally, we can calculate the activity of the sample:

A = λN = (9.98 x 10^-7 s^-1) x (4.59 x 10^14 atoms) = 4.59 x 10^7 atoms/s = 4.59 x 10^1 MBq/s

Note: MBq/s stands for megabecquerels per second, which is a unit of activity commonly used in nuclear medicine.

If the Decay Constant for 131I Is 9