Question

In March 2011, an earthquake and tsunami off the coast of northeast Japan crippled nuclear reactors at a power station in Fukashima, Japan. The resulting explosions and fires released ¹³³Xe into the atmosphere. Determine the radioactivity in 7.8 mg of this radionuclide (t_1/2= 5.25 days) in becquerels and in millicuries.

Answer 1

Activity = Number of atoms desintegrated per second

Get "K" rate constant in seconds

HL = ln(2) / k

k = ln(2) / HL

k = ln(2) / (5.25days)

k = ln(2) / (5.25*24*60*60)

k = 0.0000015281 1/s

k = 1.5281*10^-6 s^-1

now...

Find total amount of atoms:

m = 7.8 mg = 7.8*10^-3 g

MW of Xe = 132.9059107

mol = mass/MW = (7.8*10^-3)/(132.9059107) = 0.00005868813 mol

now, change to atoms

1 mol = 6.022*10^23

0.00005868813 mol --> 0.00005868813*(6.022*10^23) = 3.5341992*10^19 atoms

Activity = k * Atoms

Activity = (1.5281*10^-6 ) (3.5341992*10^19) = 5.400*190^13 atoms desintegrated per second

B)

recall that

1 Bq = 1 atom desintegrated per second

so

5.400*10^13 Bq

B)

recall that

1 Cu = 3.7e+10 Bq

x Cu = 5.400*10^13 Bq

x = (5.400*10^13) * 1/(3.7*10^10) = 1459.459 Cu

1 Cu = 1000 mCu

1459.459 Cu = 1459.459*1000 = 1459459 mCu = 1.459*10^6 mCu