The answer is 3.75 g.
Half-life is the time required for the amount of a sample to half its value.
To calculate the fraction of the sample remained unchanged, 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 N-16 is 7.13.
So, we know:
t = 28.8 s
\(t_{1/2}\) = 7.13 s
We need:
n = ?
x = ?
We could first use the second equation, to calculate n:
If:
\(t_{1/2} = \frac{t}{n}\),
Then:
\(n = \frac{t}{ t_{1/2} }\)
⇒ \(n = \frac{28.8 s}{7.13 s}\)
⇒ \(n=4.04\)
⇒ n ≈ 4
Now we can use the first equation to calculate the remained amount of the sample.
\((1/2)^{n} = x\)
⇒ \(x=(1/2)^4\)
⇒\(x= \frac{1}{16}\)
If the fraction of the sample is 1/16 = 6.25%, then the mass of the sample could be calculated as:
x g : 6.25% = 60 g : 100%
x =
