Question

Extend your thinking: The slow decay of radioactive materials can be used to find the age of rocks, fossils, and archaeological artifacts. In a process called radiometric dating, scientists measure the proportions of radioactive atoms and daughter atoms in an object to determine its age. Carbon-14 is a useful isotope because it is found in wood, ash, bone, and any other organic materials. You can use the Half-life Gizmo to model the decay of Carbon-14, which has a half-life of approximately 6,000 years (actual value is 5,730 years). In the Gizmo, select User chooses half-life and Theoretical decay. Set the Half-life to 6 seconds (to represent 6,000 years) and the Number of atoms to 100. Use the Gizmo to estimate the age of each of the objects below. For these questions, each second in the Gizmo represents 1,000 years. Description Age (years) Egyptian papyrus with 63% of its original carbon-14 atoms Aboriginal charcoal with 22% of its original carbon-14 atoms. Mayan headdress with 79% of its original carbon-14 atoms Neanderthal skull with 3% of its original carbon-14 atoms

Answer 1

The age in years of the Egyptian papyrus, the Aboriginal charcoal, the Mayan headdress, and the Neanderthal skull are 4000 years, 13106.5years , 2040 years, and 30353 years respectively.

What is the half-life of a radioactive material?

The half-life of a radioactive material is the time taken for half the atoms present in the material to decay or disintegrate.

The half-life, $t_\frac{1}{2}$, the age, t, and amount remaining, $A_{r}$, of a radioactive material are related by the formula below:

• $t = \frac{t_\frac{1}{2}*A_{r}}{-ln2}$

Half-life of carbon-14 = 6000 years

For the Egyptian papyrus with 63% of its original carbon-14 atoms:$t = \frac{6000*0.63}{-0.63} = 4000\:years$

For the Aboriginal charcoal with 22% of its original carbon-14 atoms:

$t = \frac{6000*0.22}{-0.63} = 13106.5\:years$

For the Mayan headdress with 79% of its original carbon-14 atoms:

$t = \frac{6000*0.79}{-0.63} = 2040\:years$

Neanderthal skull with 3% of its original carbon-14 atoms:

$t = \frac{6000*0.03}{-0.63} = 30353\:years$

Therefore, the age in years of the Egyptian papyrus, the Aboriginal charcoal, the Mayan headdress, and the Neanderthal skull are 4000 years, 13106.5years , 2040 years, and 30353 years respectively.

Learn more about half-life at: brainly.com/question/26689704

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