Assume a sample of^99 m Tc (lambda = 3.22 times 10^-5 s^-1) with 20 mCiradioacti

Question

Assume a sample of^99 m Tc (lambda = 3.22 times 10^-5 s^-1) with 20 mCiradioactivity. How many nuclei of^99m Tc are present in this sample? This radioactive source is injected into a patient. What is the radioactivity 60 min after the injection? We assume the gamma-ray energy is 140keV, and 10% of the gamma rays are absorbed by patient body with weight of 150kg. What is the total radiation dose: assuming that the metabolic clearance rate is of the order of days, i.e. all radiation has been released?

Explanation / Answer

a) we know that

rate = K[A]

20mCi = 740000000 = 3.22 X 10^-5 X [A]

[A ] = 2.29 X 10^13 nuclei

2) Radioactivity after 60 minutes

At = A0 e^-Kt

lnAt/A0 = -Kt

ln A0/A = kt

ln A0/A = 3.22 X 10^-5 X 60 X 60 = 0.116

Taking antilog

A0 / A = 1.122

A = A0 / 1.122 = 2.29 X 10^13 / 1.122 = 2.04 X 10^13

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