Calculating Half-life Question

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In summary, a man's body was found in a glacier in the Alps in 1991 and carbon-14 analysis revealed that it was approximately 5295 years old. This was calculated using the half-life equation, with the original carbon-14 ratio being 52.7%.
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wilson_chem90
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Homework Statement


In 1991, hikers found the frozen remains of a man in a glacier in the Alps, near the Austrian-Italian border. Carbon-14 analysis of tissue samples taken from the body revealed that the ratio of carbon-14 was 52.7% of what it was originally. Calculate the age of the body.


Homework Equations


N = No (1/2) (t/T(1/2))
(half-life equation)


The Attempt at a Solution


First I rearranged N = No (1/2) (t/T(1/2)) and adding the information to it.
I got t = 5730 yrs [log(0.527) / log(.5)]

after i did the calculations i found that
t = 5295 yrs.

So the age of the body should be approx. 5295 yrs old.

Can someone confirm please? thanks
 
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  • #2
Your result seems correct.
 
  • #3
thanks
 

What is half-life?

Half-life is the amount of time it takes for half of a radioactive substance to decay into a stable form.

How is half-life calculated?

Half-life is calculated using the following 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.

What factors affect the half-life of a substance?

The half-life of a substance can be affected by its physical and chemical properties, as well as external factors such as temperature, pressure, and the presence of other substances.

How does half-life relate to radioactive decay?

Half-life is directly related to radioactive decay, as it is the measure of time for half of a radioactive substance to decay into a stable form. As the half-life decreases, the rate of decay increases.

Why is calculating half-life important?

Calculating half-life is important in various fields such as nuclear science, medicine, and archaeology. It helps in understanding the behavior and properties of radioactive substances, as well as in determining the age of artifacts and the effectiveness of medical treatments.

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