Question

131I (300 MBq) in the chemical form of sodium iodide (NaI) has been prepared at 7:00 am this morning for a patient’s thyroid therapy treatment at 1:00 pm. The amount of radioactivity required for this patient’s therapy is to be within the range of 148 to 370 MBq. How much radioactivity is present in the dose at this scheduled treatment time? If the patient was delayed getting to her appointment for treatment by an additional 4 hours is there still sufficient amount of the radioisotope present in the dose at 5:00 pm to accomplish the therapy within the MBq dose range required? Show your work please!

Answer 1

A = A_oe^(-λt) (First order decay equation)

A_o = 300 MBq

Half life of ¹³¹I = 8.04 days = 192.96 hours

Decay constant, λ = 0.693/ t_1/2

λ = 0.693 / 192.96 h = 3.59x10^-3 h^-1

t = 6 hours

A = A_oe^(-λt)

A = 300 MBq x e^{(-3.59x10-3 h-1 x 6 h)}

A =300 MBq x e^(-0.02154)

A = 300 MBq x 0.978

A = 293.4 MBq

The amount of activity after six hours is 293.4 MBq (within 148 to 370 MBq)

Delay of additinal 4 hours (Dose at 5:00 pm)

t = 10 h (6h + 4 h)

A = A_oe^(-λt)

A = 300 MBq x e^{(-3.59x10-3 h-1 x 10 h)}

A =300 MBq x e^(-0.0359)

A = 300 MBq x 0.964

A = 289.2 MBq

The amount of activity after additional four hours is 289.2 MBq (within 148 to 370 MBq)