# Half Life - Calculate Fraction Remaining

• jendrix
In summary, using the second equation gives a result that is closer to the original problem. However, the answer may be rounded off to a number that is not exactly 0.757069666.
jendrix

## Homework Statement

Carbon 14 has a half-life of 5730 years, what fraction will have decayed in 2300 years?

Nf/No =e^-kt

## The Attempt at a Solution

Nf/No =e^-1.21 x 10^-4 x 2300

=0.068585374

However if I use Nf =No(1/2)^2300/5730

I get 0.757125224

I appreciate that I'm looking for the fraction that has decayed but I'm unsure as to why this has produced 2 different answers, I thought either could be used for this problem.

Thanks

jendrix said:
Nf/No =e^-1.21 x 10^-4 x 2300

=0.068585374
Redo this.

Recheck your math for the first formula.

EDIT: Doc Al beat me to it again.

I agree with them guys. You got it right using the second method jendrix. But maybe just a mistake while calculating using the first method.

Hi, I think I was using a wrong value for the decay constant but somehow wrote it down correct here.

I was wondering why there is a discrepancy albeit a small one depending on which formula I use, is it to do with the rounding of the constant?

jendrix said:
Hi, I think I was using a wrong value for the decay constant but somehow wrote it down correct here.

I was wondering why there is a discrepancy albeit a small one depending on which formula I use, is it to do with the rounding of the constant?
You're still making an error somewhere. Just evaluate the formula you gave in your first post:
jendrix said:
Nf/No =e^-1.21 x 10^-4 x 2300
That should give you the right answer.

Thanks Doc Al, I now get 0.757069666 as opposed to 0.757125224 from the other formula.
Is this where rounding the constant has had an effect?

Now I have to find the fraction that was lost to decay, if i do 1 - 0.757069666 to give 0.242930334 would you consider this sufficient or should I call it 6/25?

jendrix said:
Thanks Doc Al, I now get 0.757069666 as opposed to 0.757125224 from the other formula.
Is this where rounding the constant has had an effect?
Yes. (But round off your answers to a reasonable number of significant figures.)
Now I have to find the fraction that was lost to decay, if i do 1 - 0.757069666 to give 0.242930334 would you consider this sufficient or should I call it 6/25?
That decimal should be fine (rounded off, of course). (When they say 'fraction' they probably don't literally mean fraction, as in numerator/denominator.)

Excellent, thanks for all your help guys

## 1. What is half-life and how is it calculated?

Half-life is the time it takes for half of a given sample of a radioactive substance to decay. It is calculated using the formula t1/2 = ln(2) / λ, where t1/2 is the half-life, ln(2) is the natural logarithm of 2, and λ is the decay constant.

## 2. How do you calculate the fraction remaining after a certain number of half-lives?

The fraction remaining can be calculated using the formula Nt / N0 = (1/2)n, where Nt is the amount remaining after n half-lives, and N0 is the initial amount.

## 3. Does the half-life of a substance change over time?

No, the half-life of a substance remains constant and does not change over time. It is an inherent property of a radioactive substance.

## 4. How is half-life used in radiometric dating?

Half-life is used in radiometric dating to determine the age of rocks and other geological materials. By measuring the amount of a radioactive isotope in a sample and calculating the fraction remaining, scientists can estimate how long it has been since the material was formed.

## 5. Can half-life be used to predict the exact time of decay for a single atom?

No, half-life can only be used to predict the average time it takes for a large group of atoms to decay. The exact time of decay for a single atom is random and cannot be predicted.

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