Question

A piece of wood from an ancient Egyptian tomb is tested for its carbon-14 activity. It is found to have an activity per gram of carbon of A=10decay/min⋅gA=10decay/min⋅g. Carbon-14 has an initial activity of 15decay/min⋅g15decay/min⋅g and a half-life of 5730 years. In years, what is the age of wood?

Answer 1

The age of the wood can be determined using the formula t = (t(1/2) / ln(2)) * ln(A0 / A) where t is the age, t(1/2) is the half-life, A0 is the initial activity, and A is the current activity. Plugging in the values, the age of the wood is approximately 3720 years.

Step-by-step explanation:

The age of the wood can be determined by comparing the current carbon-14 activity per gram of carbon with the initial activity. In this case, the wood has an activity of 10 decay/min⋅g and the initial activity is 15 decay/min⋅g. Carbon-14 has a half-life of 5730 years. To find the age, we can use the formula:

t = (t(1/2) / ln(2)) * ln(A0 / A)

where t is the age, t(1/2) is the half-life, A0 is the initial activity, and A is the current activity. Plugging in the values, we get:

t = (5730 / ln(2)) * ln(15 / 10) ≈ 3720 years

Therefore, the age of the wood is approximately 3720 years.