Final Review Bonus Problem 28 Bonus Problem 28 The iodine isotope I is used in h

Question

Final Review Bonus Problem 28 Bonus Problem 28 The iodine isotope I is used in hospitals for diagnosis of thyroid function. 752 Aug are ingested by a patient. The half-life the iodine isotope 131 I is 8.0207 days and mass is 130.906 u. Resources v previous l 28 of 29 l next Part A Determine the activity immediately after ingestion. Express your answer using three significant figures. dN decays/s dt 10 Submit My Answers Give Up Part B Determine the activity 1.00 h later when the thyroid is being tested. Express your answer using three significant figures. N decays/s Submit My Answers Give up

Explanation / Answer

Decay constant = lambda = 0.693/Thalf

Thalf = 8.0207 days = 692988.48 sec

lambda = 0.693/692988.48 = 1.000016*10^-6 sec^-1

Now nuclei of Iodine initially is

N/Na = moles

N = moles*Na

N = (752*10^-6/130.906)*6.023*10^23

N = 3.459960*10^18 nucleis

Now using the activity formula

dN/dt = lambda*N

dN/dt = 1.000016*10^-6*3.459960*10^18

dN/dt = 3.46*10^12 decays/sec

B.

Now after 1 hr activity will be

1 hr = 3600 sec

N = N0*exp(-lambda*t)

N = 3.46*10^12*exp(-1.000016*10^-6*3600)

N = 3.447*10^-12 decays/sec

C.

after 4 months

4 month = 1.0368*10^7 sec

N = 3.46*10^12*exp(-1.000016*10^-6*1.0368*10^7)

N = 1.087*10^8 decays/sec

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