Question

Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about 68% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. (Round your answer to the nearest hundred years.)

Answer 1

Answer:

• 28,700 years

1. Data:

a) Half-life: 5730 years

b) Final radioactivity: 68%

2. Solution:

a) Determine the number of half-lives undergone

• Since, the radioactivity has decreased to 68%, means that the carbon-14 contanined is has been reduced in 32%: 100% - 68% = 32%.

• 32 = 2⁵, meaning that five half-lives have passed since the plant material that formed the parchment fragment died.

b) Compute the time of five half-lives:

• 5 × half-life time = 5 × 5730 years = 28,650 years.

c) Round to the nearest hundred:

• 28,650 years ≈ 28,700 years

And that is the age of the parchment.