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Chapter 19: Problem 36

Fresh rainwater or surface water contains enough tritium \(\left({ }_{1}^{3} \mathrm{H}\right)\) to show \(5.5\) decay events per minute per \(100 . \mathrm{g}\) water. Tritium has a half-life of \(12.3\) years. You are asked to check a vintage wine that is claimed to have been produced in \(1946 .\) How many decay events per minute should you expect to observe in \(100 . \mathrm{g}\) of that wine?

Short Answer

Expert verified
You should expect to observe approximately \(0.15\) decay events per minute in \(100g\) of the wine if it was produced in \(1946\).

Step by step solution

01

Find the time elapsed since the wine was produced

First, we need to know the age of the wine to find out how much tritium has decayed. We can calculate this by subtracting the production year from the current year. (Assume the current year is 2022). Age of the wine = Current year - Production year Age of the wine = 2022 - 1946 = 76 years
02

Calculate the number of half-lives elapsed

Given the half-life of tritium is 12.3 years, we can calculate the number of half-lives that have elapsed since the wine was produced. Number of half-lives = Age of the wine / half-life of tritium Number of half-lives = 76 years / 12.3 years = 6.17886179
03

Use the decay formula to find the decay rate

The decay formula for radioactive substances is: Final decay rate = Initial decay rate × (1/2)^(number of half-lives) In this case, the initial decay rate is given as 5.5 decay events per minute per 100g water. Final decay rate = 5.5 × (1/2)^6.17886179 Final decay rate ≈ 0.14846 decay events per minute per 100g water
04

Round the result and write the conclusion

Round the final decay rate to two decimal places: Final decay rate ≈ 0.15 decay events per minute per 100g water In conclusion, if the vintage wine was indeed produced in 1946, you should expect to observe approximately 0.15 decay events per minute in 100g of the wine.

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Most popular questions from this chapter

Strontium-90 and radon-222 both pose serious health risks. \({ }^{90} \mathrm{Sr}\) decays by \(\beta\) -particle production and has a relatively long half-life (28.9 years). Radon-222 decays by \(\alpha\) -particle production and has a relatively short half-life (3.82 days). Explain why each decay process poses health risks.

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