Question

What mass of a 60.0-gram sample of N-16 will remain unchanged after 28.8 seconds?

Answer 1

Without the half-life of N-16, it's impossible to determine the mass of a 60.0-gram sample of N-16 that will remain after 28.8 seconds.

Step-by-step explanation:

The question asks us to calculate the mass of N-16 that will remain unchanged after 28.8 seconds, given the initial mass and the fact that N-16 is a radioactive isotope. Unfortunately, since the half-life of N-16 is not provided in the question or any additional information, we cannot proceed with the calculations. Consequently, without knowing the half-life, it is impossible to give an accurate answer to how much of the 60.0-gram sample of N-16 will remain after 28.8 seconds.

Answer 2

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

`n = (t)/( t_(1/2) )`
⇒
`n = (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= (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 =