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:
n - a number of half-lives
x - a remained fraction of a sample
2. \(t_{1/2} = \frac{t}{n}\)
where:
\(t_{1/2}\) - half-life
t - total time elapsed
n - a number of half-lives
The half-life of Sr-90 is 28.8 years.
So, we know:
t = 87.3 years
\(t_{1/2}\) = 28.8 years
We need:
n = ?
x = ?
We could first use the second equation, to calculate n:
If:
\(t_{1/2} = \frac{t}{n}\),
Then:
\(n = \frac{t}{ t_{1/2} }\)
⇒ \(n = \frac{87.3 years}{28.8 years}\)
⇒ \(n=3.03\)
⇒ n ≈ 3
Now we can use the first equation to calculate the remained amount of the sample.
\((1/2)^{n} = x\)
⇒ \(x=(1/2)^3\)
⇒\(x= \frac{1}{8}\)
