Calculate a Building's Age Using Nickel-63 Decay

Chapter 10, Problem 17

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QUESTION: An archaeologist sometime in the future analyzes the iron used in an old building. The iron contains tiny amounts of nickel-63, with a half-life of 92 years. On the basis of the amount of nickel-63 and its decay products found, it is estimated that about 0.78% (1/128) of the original nickel-63 remains. If the building was constructed in 1980, in what year did the archaeologist make the discovery?

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Calculate a Building's Age Using Nickel-63 Decay
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The scenario involves an archaeologist analyzing iron in an old building containing nickel-63, which has a known half-life of 92 years. With only 0.78% of the original nickel-63 remaining, the goal is to estimate the year when this discovery was made. We delve into the calculations and principles of first-order decay reactions.

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QUESTION: An archaeologist sometime in the future analyzes the iron used in an old building. The iron contains tiny amounts of nickel-63, with a half-life of 92 years. On the basis of the amount of nickel-63 and its decay products found, it is estimated that about 0.78% (1/128) of the original nickel-63 remains. If the building was constructed in 1980, in what year did the archaeologist make the discovery?

ANSWER:

Step 1 of 2

The concept of half-life is crucial for understanding the decay of nuclear elements. It represents the time span necessary for half of the initial nuclei to decay. This, along with the quantity of decayed metals, helps us analyze the time span that has passed.

Given data:

The half-life of nickel-63 is 92 years.

The amount of nickel-63 remaining is 0.78% (1/128).

The year in which the building is constructed is 1980.

We have to estimate the time required to decay nickel-63 and remain only 0.78 %. For that, we have to estimate the K for the decay reaction.

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