a) What order of kinetics does this follow (show your work)? b) What fraction of

Question

a) What order of kinetics does this follow (show your work)?

b) What fraction of Polonium 210 would remain after one year?

c) 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 µg 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)Radioactive decay is a first-order process

Radioactive decay follows the following first-order law:

C = Coe-kt

where

C = activity at time t (sometimes you see it as Ct)
Co = initial activity (that is, when t = 0)
k = the decay constant
t = time

We can rearrange the above equation to give "k"

Rearrange to get:

C/Co = e-kt

Take the natural log of both sides:

ln (C/Co) = ln (e-kt)

ln (C/Co) = -kt

Given data ; (C/Co) = 0.5   and t = 138 days= 0.378 yr . We can calculate k:

In(0.5) = -kt   and   k= -ln(0.5)/0.378yr = -ln(0.5)/0.378yr = 1.83 yr-1 .

In addition, considering "t1/2" (the half-life), you can also use

k = (ln 2) / t1/2 = 1.83 yr-1

b) After 1 year we can use the previous equation:

Rearrange to get:

C/Co = e-kt

C1yr/Co = e-kt = e-(1.83 yr-1)(1 yr) = e-(1.83) = 0.1604 .... 16.04% remaining

c) Given data : C45 = 1.1 microg

We have to convert 45 days in years: 45 days(1 yr/365days) = 0.123yr

Then:

C45/Co = e-kt = e-(1.83 yr-1 )( 0.123yr )= e-(0.2251) = 0.7984.... 79.84% remaining

Then C0 = (1.1microg)/(0.7984) = 1.38 microg

Dose of Po that was administered to the person = 1.38 microg

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