Question

The half-life of radioactive substance is 2.5 minutes. what fraction of the origional radioactive remains after 10 mins

Answer 1

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

`n = (t)/( t_(1/2) )`
⇒
`n = (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= (1)/(16)`