Question

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

Answer 1

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:
$n * log(1/2) = log(0.125)$
$n = \frac{log(0.125)}{log(1/2)}$
$n = \frac{log(0.125)}{log(0.5)}$
$n= \frac{-0.903}{-0.301}$
$n = 3$

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

Answer 2

Answer:

3

Explanation: