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Answer:
3 half-lives 7. An isotope of Cesium (Cesium-137) has a half life of 30 years. If 1.0 mg of cesium-137 disintegrates over a period of 90 years, how many mg of cesium-137 would remain? of sodium-25 is 60 seconds? : 3 minutes t=601 = 3 half-lives 5.0mg ~ 2.5 mg + 1.25mg →) 625 mg.
Explanation:
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- To find the mass in grams of Cesium that would remain after disintegration, we would be applying the formula:
- N(t) = [tex]N_{0} (\frac{1}{2})^{\frac{t}{t{\frac{1}{2} } }[/tex]
where:
[tex]N_{0}[/tex] = Initial quantity of the sample = 1.0g
t = time in years of disintegration = 90 years
[tex]t\frac{1}{2}[/tex] = Half life of cesium isotope = 30 years
N(t) = Quantity of substance after disintegration = ?
- Solving for N(t)
N(t) = [tex]1 ( \frac{1}{2})^ \frac{90}{30}[/tex]
N(t) = [tex]1 (\frac{1}{2})^{3}[/tex]
N(t) = 0.125 grams
Therefore, the quantity of cesium-137 that would remain after disintegrating over a period of 90 years is 0.125 grams.
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