Question

A patient ingests 140 mg of 131I (iodine-131), a beta emitter with a half-life of 8.0 days. Assuming that none of the 131I is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those 4.0 hours? Express your answer using two significant figures.

exposure= _____ Ci

Answer 1

we know that

rate constant (k) = ln2 / t1/2

given

t1/2 = 8 days

= 8 x 24 hr

t1/2 = 192 hr

so

k = ln2 /192

k = 3.61 x 10-3

now

moles = mass / molar mass

so

moles of I = 140 x 10-3 / 131

moles of I = 1.0687 x 10-3

now

number of molecules = moles x 6.023 x 10^23

so

number of molecules = 1.0687 x 10-3 x 6.023 x 10^23

number of molecules = 6.4368 x 10^20

now

N = No x e^(-kt)

so

N = 6.64368 x e^(-3.61 x 10-3 x 4)

N = 6.5484346 x 10^20

now

exporsue = (No - N) / t

exposure = (6.64368 x 10^20 ) - ( 6.5484346 x 10^20 ) / 4 x 60 x 60

exposure = 6.614265 x 10 ^14 decays / second

now

we know that

1 Ci = 3.7 x 10^10 decays / second

so

exposure = 6.614265 x 10^14 / 3.7 x 10^10

exposure = 17,876.4 Ci

so

the exposure = 17876.4 Ci = 1.8 x 10^4 Ci