The answer is 1/16.
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
So, we know:
t = 10 min
\(t_{1/2}\) = 2.5 min
We need:
n = ?
x = ?
We could first use the second equation to calculate n:
If:
\(t_{1/2} = \frac{t}{n}\),
Then:
\(n = \frac{t}{ t_{1/2} }\)
⇒ \(n = \frac{10 min}{2.5 min}\)
⇒ \(n=4\)
Now we can use the first equation to calculate the remained fraction of the sample.
\((1/2)^{n} = x\)
⇒ \(x=(1/2)^4\)
⇒\(x= \frac{1}{16}\)
