Question

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

Answer 1

Approximately 12.5% of the Sr-90 sample remains unchanged after 87.3 years.

Step-by-step explanation:

The fraction of a Sr-90 sample that remains unchanged after 87.3 years can be calculated using the concept of half-life. The half-life of Sr-90 is 28.1 years, which means that after each half-life, half of the sample decays. To find the fraction remaining, divide the elapsed time by the half-life:

(Elapsed time) / (Half-life) = (87.3 years) / (28.1 years) ≈ 3.1

This means that approximately 3.1 half-lives have occurred in 87.3 years. Since half of the sample decays each half-life, the fraction remaining after 3.1 half-lives is approximately 0.5 × 0.5 × 0.5 ≈ 0.125. Therefore, approximately 12.5% of the Sr-90 sample remains unchanged after 87.3 years.

Answer 2

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) = (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) = (t)/(n)`,
Then:

`n = (t)/( t_(1/2) )`
⇒
`n = (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= (1)/(8)`