Question

If the half-life of 201Tl is 3.0 days what is it activity in megabecquerels after 3.0 days

Answer 1

HL of Tl = 3 days

find activit in megabecquerels after t = 3 days

Activity = k * sample

if HL = 3 days = 3*24*3600 s = 259200 s

assume 1st order deacay:

HL = ln(2)/k

k = ln(2) / HL = ln(2) / 259200 = 0.00000267417 1/s

now...

no initial mass is givenj, so assume 1 mol of species initially

then, after t = 3 days, mol left = 50%*1 = 0.5 mol left

change to atoms

atoms = mol*NA = (0.5)(6.022*10^23) = 3.011*10^23 atoms of Tl left

activity = k*atoms = 0.00000267417 * 3.011*10^23 = 8.05192*10^17 Bq

change to MBq --< (8.05192*10^17 ) /(10^6) = 8.05192*10^11 MBq

this is per unit mol, that is, if initial mass of Tl = 201 g, then activity will be 8.05192*10^11 MBq after t = 3 days