Answer to Question #249669 in Other for chaba

Question

1.    It is estimated that the Chernobyl disaster released 6.0 Megacurie of ¹³⁷Cs (half life 30.2yrs) into the environment.

a)   How much activity does Cs have in the year 2021?

b)   Calculate the mass of Cs released?

Answer 1

We can calculate the mass released using Avogadro’s number and the concept of a mole if we can first find the number of nuclei N released. Since the activity R is given, and the half-life of ¹³⁷Cs is found to be 30.2 years, we can use the equation

R = 0.693 / Nt_1/2 to find N.

Solving the equation R = 0.693 / Nt_1/2 for N gives N = Rt_1/2 / 0.693

Entering the given values yields

N = ((6.0 MCi) x (30.2 y)) / 0.693

Converting curies to becquerels and years to seconds, we get

N = ((6.0 × 106 Ci) (3.7 × 1010 Bq/Ci) (30.2 y) (3.16×107 s/y)) / 0.693 = 3.1×10²⁶

One mole of a nuclide ^AX has a mass of A grams, so that one mole of ¹³⁷Cs has a mass of 137 g. A mole has 6.02 ×10²³ nuclei. Thus the mass of ¹³⁷Cs released was

m = (137 g / 6.02×10²³) (3.1×10²⁶) = 70 × 10³ g = 70 kg