# Problem: Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is 9 18F⟶ 8 18O + +10e)Physicians use 18F to study the brain by injecting a quantity of fluoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.(b) If a sample of glucose containing radioactive fluorine-18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?

🤓 Based on our data, we think this question is relevant for Professor Briggs' class at ASU.

###### FREE Expert Solution

We can determine [A]t, but lack the value of k.

can be obtained from the equation of half-life for 1st order reactions:

Step 1: We rearrange the half-life equation to solve for k :

$\overline{){\mathbf{k}}{\mathbf{=}}\frac{\mathbf{ln}\left(2\right)}{{\mathbf{t}}_{\mathbf{1}}{\mathbf{2}}}}}$

6.32×10-3 min-1

Step 2: We convert the time elapsed to minutes:

335.4 min

Step 3: We determine [A]t in the 1st Order Rate Law:

ln [A]t = -2.119728

Ln has a base of e. When you divide a number by ln you will take e to the power of the number.

###### Problem Details

Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is 9 18F⟶ 8 18O + +10e)
Physicians use 18F to study the brain by injecting a quantity of fluoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.

(b) If a sample of glucose containing radioactive fluorine-18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Identifying Reaction Order concept. If you need more Identifying Reaction Order practice, you can also practice Identifying Reaction Order practice problems.

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Based on our data, we think this problem is relevant for Professor Briggs' class at ASU.

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Our data indicates that this problem or a close variation was asked in Chemistry - OpenStax 2015th Edition. You can also practice Chemistry - OpenStax 2015th Edition practice problems.