A 0.6-kg sample of a wooden artifact has an activity of 2.00 *10³ decays per minute.What is the age of the artifact? Note that living material has an activity of 15.0 decays/minute per gram of carbon present,and T_1/2 for ¹⁴C is 5730 yr. A)12,434 yr B)8,618 yr C)18,164 yr D)12,590 yr

Question

Quizplus · Accepted Answer

First, we need to convert the activity of the wooden artifact from decays per minute to decays per gram of carbon. 
Using the activity of living material (15.0 decays/minute per gram of carbon present) as a standard, we can calculate the amount of carbon present in the wooden artifact:

2.00 decays/minute 
--------------------- = 0.133 g of carbon 
15.0 decays/minute per g

Next, we can use the radioactive decay equation to calculate the age of the artifact:

N/N0 = e^(-λt), where 
N = the remaining amount of carbon-14 
N0 = the original amount of carbon-14 
λ = the decay constant (ln(2)/t1/2, where t1/2 is the half-life) 
t = the age of the artifact

We know that N/N0 = 0.5 (i.e. half of the carbon-14 has decayed) and that the half-life of carbon-14 is 5730 years:

0.5 = e^(-ln(2)*t/5730)

Solving for t:

t = -(5730/ln(2)) * ln(0.5) 
t ≈ 12,434 years

Therefore, the age of the artifact is approximately 12,434 years.

​A 06-Kg Sample of a Wooden Artifact Has an Activity of of 2.00

A 06-Kg Sample of a Wooden Artifact Has an Activity of of 2.00