A 95 kg patient swallows a 35 Ci beta emitter whose half-life is 5.0 days and wh

Question

A 95 kg patient swallows a 35 Ci beta emitter whose half-life is 5.0 days and whose RBE is 1.6. The beta particles are emitted with an average energy of 0.35 MeV, 90% of which is absorbed by the body. You are a health care worker needing to find the patient's dose equivalent after one week. These series of steps will help you find that dose equivalent. In all questions, assume the radioactive nuclei are distributed throughout the patient's body and are not being excreted. How many radioactive nuclei did the patient swallow?

Explanation / Answer

dN / dt = -lambda*N

dN / dt = 35*10^(-6) * 3.7*10^10 Bq

dN / dt = 129.5*10^4 Bq

lambda = ln(2) / t1/2

lambda = 0.693 / 5*24*3600 = 1.605*10^(-6) / s

radioactive nuclei swallowed by patient,

N = 129.5*10^4 / 1.605*10^(-6)

N = 80.68*10^10

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