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kramer
3 years ago
7

What fraction of a Sr-90 sample remains unchanged after 87.3 years

Chemistry
1 answer:
jolli1 [7]3 years ago
8 0
The answer is 1/8.

Half-life is the time required for the amount of a sample to half its value.
To calculate this, we will use the following formulas:
1. (1/2)^{n} = x,
where:
<span>n - a number of half-lives
</span>x - a remained fraction of a sample

2. t_{1/2} = \frac{t}{n}
where:
<span>t_{1/2} - half-life
</span>t - <span>total time elapsed
</span><span>n - a number of half-lives
</span>
The half-life of Sr-90 is 28.8 years.
So, we know:
t = 87.3 years
<span>t_{1/2} = 28.8 years

We need:
n = ?
x = ?
</span>
We could first use the second equation, to calculate n:
<span>If:
t_{1/2} = \frac{t}{n},
</span>Then: 
n = \frac{t}{ t_{1/2} }
⇒ n = \frac{87.3 years}{28.8 years}
⇒ n=3.03
<span>⇒ n ≈ 3
</span>
Now we can use the first equation to calculate the remained amount of the sample.
<span>(1/2)^{n} = x
</span>⇒ x=(1/2)^3
⇒x= \frac{1}{8}<span>
</span>
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