The cloth shroud from around a mummy is found to have a carbon-14 activity of 8.1 disintegrations per minute per gram of carbon as compared with living organisms that undergo 15.2 disintegrations per minute per gram of carbon.
From the half-life for carbon-14 decay, 5715 yr, calculate the age of the shroud.
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k = 0.693/t1/2
k = 0.693/5715yr = 1.213E-4
Substitute k into the below equation.
ln(No/N) = kt
No = 15.2
N = 8.1
k from above.
Solve for t (in years).
Thanks.
To calculate the age of the shroud, we can use the formula for exponential decay:
N = N0 * (1/2)^(t / t1/2)
Where:
N = Final amount of carbon-14 activity in the shroud
N0 = Initial amount of carbon-14 activity in a living organism (15.2 disintegrations per minute per gram of carbon)
t = Time elapsed since the death of the organism (age of the shroud)
t1/2 = Half-life of carbon-14 (5715 years)
In this case, N = 8.1 disintegrations per minute per gram of carbon, and N0 = 15.2 disintegrations per minute per gram of carbon. We need to find the value of t.
Let's rearrange the formula to solve for t:
t = t1/2 * log2 (N / N0)
Substituting the given values:
t = 5715 years * log2 (8.1/15.2)
Using a calculator, we can determine:
t ≈ 5715 years * (-0.439)
t ≈ -2509 years
Since a negative age does not make sense in this context, we can conclude that this calculation suggests that the shroud is not 2509 years old. However, note that this calculation assumes a constant decay rate, which may not be the case due to various factors such as contamination or changes in the environment. Additionally, this calculation does not account for any fluctuations in carbon-14 levels over time. Therefore, it is essential to consider such factors and use other dating methods to determine the actual age of the shroud.