The activity at 1 pm when the patient is injected is 6.3 mCi.
A quantity's half-life is the amount of time needed for it to decrease to half of its initial value.
The half-life of an isotope is 1.8 hours.
The sample prepared at 10 am has an activity of 20 mCi.
Now, the variation of activity with time is given as:
[tex]R = R_0 (\frac{1}{2} )^{ \frac{t}{t_{t_{1/2}} }[/tex]
We have, R₀ = 20 mCi
The half-life, [tex]t_{\frac{1}{2} } = 1.8 {~}\text{hours}[/tex]
Now, the activity is calculated at 1 pm.
So, t = 1 pm - 10 am = 3 hrs
Therefore, the activity at 1 pm will be:
[tex]R = R_0 (\frac{1}{2} )^{ \frac{t}{t_{t_{1/2}} }[/tex]
[tex]R = 20 \times (\frac{1}{2} )^{\frac{3}{1.8} }[/tex]
[tex]R = 20 \times (\frac{1}{2} )^{1.67}[/tex]
R = 20 × 0.31425334363
R = 6.28 mCi
R = 6.3 mCi
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