Radioactive Polonium (Po) 210 decays with a half-life of 138 days (in other word

Question

Radioactive Polonium (Po) 210 decays with a half-life of 138 days (in other words C/Co = 0.5 after 138 days). What order of kinetics does this follow (show your work)? What fraction of Polonium 210 would remain after one year? Polonium has occasionally been implicated in high profile international poisonings, such as Victor Litvinenko. If during an autopsy, a cadaver's body contains a total of 1.1 mug of Po 210 and it is suspected that the poisoning occurred 45 days prior to the autopsy, what is the likely dose of Po that was administered to the person?

Explanation / Answer

a)

we know that

radioactive decays follow first order kinetics

b)

now

for first order kinetics

ln (N/No) = -kt

now

decay constant (k) = 0.693 / half life

given

half life = 138 days

so

k = 0.693 / 138

k = 5.02174 x 10-3

now

given

time (t) = 1 year = 365.25 days

so

ln (N/No) = -5.02174 x 10-3 x 365.25

ln (N/No) = -1.83419

N/No = 0.1597

so

0.1597 fraction of Polonium 210 would remain after one year

c)

now

for first oder

ln (N/No) = -kt

ln (N/No) = -5.02174 x 10-3 x 45

ln (N/No) = -0.226

N/No = 0.797735

given

N= 1.1

so

1.1 / No = 0.797735

No = 1.3789 ug

so

the likely dose of Po that was administered to the person was 1.3789 ug

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