Find the approximate age of the fragment in the following case: A fragment found in a cave believed to have been inhabited by early humans contains 0.21 times as much C-14 as an equal amount of carbon in the atmosphere when the organism containing the fragment died. The half life of C-14 is 5730 years.
- print Print
- list Cite
Expert Answers
Tushar Chandra
| Certified Educator
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
The half life of C-14 is 5730 years. In 5730 years, the amount of C-14 decreases to 1/2 the initial amount. In n*5730 years, the amount if C-14 left is given by (1/2)^n
Let the age of the fragment in the cave be n years. It is given that the fragment has 0.21 times as much C-14 as what the atmosphere had.
This gives us : 0.21 = (1/2)^n
Take the logarithm of both the sides
=> log 0.21 = log [(1/2) ^n]
=> log 0.21 = n * log (1/2)
=> n = log 0.21 / log 0.5
=> n = 2.2515
The age of the fragment is n* 5730 = 2.2515* 5730 = 12901 years.
The required age of the fragment is approximately 12901 years.
Related Questions
- If the half life of C-14 is 5730 years, what is the radio-carbon estimate of the age of a...
- 1 Educator Answer
- What is the daughter isotope of carbon-14 decay?
- 1 Educator Answer
- Estimate the age of the wood. The carbon in humans, and plants contains a small percentage of the...
- 1 Educator Answer
- When carbon burns in limited oxygen gas to form carbon monoxide gas, is the equation `C + 1/2 O_2...
- 1 Educator Answer