Question

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

Answer 1

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.
$(1/2)^{n} = x$
⇒ $x=(1/2)^3$
⇒$x= \frac{1}{8}$