What fraction of a Sr-90 sample remains unchanged after 97.3 years

What fraction of a Sr-90 sample remains unchanged after 97.3 years

Answers

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}

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