Question

A sample originally contained 1.28 g of a radioisotope. It now contains 1.12 g of its daughter isotope.

How many half-lives have passed since the sample originally formed?

3
4
8
16

Answer 1

3

Step-by-step explanation:

Answer 2

The answer is 3.

The relation between number of half-lives (n) and decimal amount remaining (x) can be expressed as:


`(1/2) ^(n) =x`

We need to calculate n, but we need x to do that. To calculate what percentage of a radioactive species would be found as daughter material, we must calculate what amount remained:
1.28 - 1.12 = 0.16

If 1.28 is 100%, how much percent is 0.16:
1.28 : 100% = 0.16 : x
x = 12.5%
Presented as decimal amount:
x = 0.125


Now, let's implement this in the equation:


`(1/2) ^(n) =0.125`

Because of the exponent, we will log both sides of the equation:

`n * log(1/2) = log(0.125)`

`n = (log(0.125))/(log(1/2))`

`n = (log(0.125))/(log(0.5))`

`n= (-0.903)/(-0.301)`

`n = 3`

Therefore, 3 half-lives have passed since the sample originally formed.