Some Radioactive Isotopes Useful in Medical Imaging Mode of Decay Half-ife Use i

Question

Some Radioactive Isotopes Useful in Medical Imaging Mode of Decay Half-ife Use in Medical Imaging Isotope C Carbon-11 Fluorine-18 Phosphorus-32 20.3 m 109 m 14.3 d Brain scan to trace glucose metabolism Brain scan to trace glucose metabolism Detect eye tumors EP C Chromium-51 Fe Iron-59 Ga Gallium-67 TSe Selenium-75 Kr Krypton-81m E.C, y 27.7 d Diagnose albinism, image the spleen and gastrointestina Bone marrow function, diagnose anemias Whole-body scan for tumors Pancreas scan La 44.5 d 78.3 h 13.35 13.3 s 22.2 m 6.01 h 8.04 d 64.1 h 3.05 d ?.?., EC., ? req Lung ventilation scan Scan for bone diseases, including cancer Brain, liver, kidney, bone scans; diagnosis of damaged hear Diagnosis of thyroid malfunction Kidney scan Heart scan and exercise stress test Strontium-81 T Technetium-99m ?, ? EC., ?.?., Iodine-131 Hg Mercury-197 29T Thallium-201 The radioactive isotope strontium-81 is used in medical imaging as indicated on the table above. 1f 71.3 milligrams of strontium-81 is administered to a patient, how many milligrams are left in the body after 88.8 minutes mg Submit Answer Retry Entire Group 9 more group attempts remaining

Explanation / Answer

Given:

Half life = 22.2 min

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(22.2)

= 3.122*10^-2 min-1

we have:

[Sr]o = 71.3 mg

t = 88.8 min

k = 3.122*10^-2 min-1

use integrated rate law for 1st order reaction

ln[Sr] = ln[Sr]o - k*t

ln[Sr] = ln(71.3) - 3.122*10^-2*88.8

ln[Sr] = 4.2669 - 3.122*10^-2*88.8

ln[Sr] = 1.4949

[Sr] = e^(1.4949)

[Sr] = 4.459 mg

Answer: 4.46 mg

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