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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

2 Answers

3 votes

Answer:

3

Step-by-step explanation:

User Stackyyflow
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8.6k points
3 votes
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.
User Ahmad Ragab
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