The iodine isotope 53 131 I is used in hospitals for diagnosis of thyroid functi

Question

The iodine isotope 53131I is used in hospitals for diagnosis of thyroid function. 732 g are ingested by a patient. The half-life the iodine isotope 53131I is 8.0207 days and mass is 130.906 u.

Part A

Determine the activity immediately after ingestion.

Express your answer using three significant figures.

Part B

Determine the activity 1.00 h later when the thyroid is being tested.

Express your answer using three significant figures.

Part C

Determine the activity 4.5 months later. Suppose that each month has 30 days.

Express your answer using two significant figures.

Explanation / Answer

A)
activity,
A = lambda * N

N is number of particle in sample = mass * Avogadro's number / molar mass
= (732*10^-6)*(6.022*10^23)/(130.906)
= 3.37*10^18 particles

lambda = 0.693/half life
= 0.693/8.0207 days
­= 0.0864 hour-1

Ao = lambda * N
= (0.0864 hour-1)*(3.37*10^18 particles)
= 2.91*10^17 particles/hour
Answer: 2.91*10^17 particles/hour

B)
t = 1 hr = 1/24 days
use:
A = Ao*e^(-lambda*t)
=( 2.91*10^17)* e^(-0.0864*1/24)
=2.90*10^17 particles/hour

C)
t = 4.5 month = 4.5*30 days = 135 days
use:
A = Ao*e^(-lambda*t)
=( 2.91*10^17)* e^(-0.0864*135)
=2.50*10^12 particles/hour

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