Sample Exercise: A Medical Isotope
Technetium-99 is a radioactive isotope with a half-life of 6.0 hours that is used in bone scans and other medical tests. It emits gamma radiation.
a. If a sample of technetium-99 is prepared a half-day (12 hours) before it is used, what fraction of the original amount of the isotope remains at the time of use.

Question

[latex]t_{\frac{1}{2}} = 6.0[/latex] h
t = 12 h

fraction remaining = ?
b. What fraction remains one day (24 hours) after preparation?

t = 24 h

fraction remaining = ?

Accepted Answer

a.

[latex]\frac{t}{t_{\frac{1}{2}}} = \frac{12 h}{6 h}=2[/latex]

fraction [latex]= \frac{1}{2}× \frac{1}{2}= \frac{1}{4}[/latex]

[latex]\frac{t}{t_{\frac{1}{2}}} = \frac{24 h}{6 h}=4[/latex]

b.

fraction [latex]= \frac{1}{2}× \frac{1}{2} × \frac{1}{2} × \frac{1}{2}= \frac{1}{16}[/latex]

Question 19.1: Sample Exercise: A Medical Isotope Technetium-99 is a radioa...

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