9. A piece of wood found in an ancient burial mound contains only half as much carbon-14 as a piece of wood cut from a living tree growing nearby. It the half-life for carbon-14 is 5730 years, what is the approximate age of the ancient wood?
Since the ancient wood has only half as much carbon-14 as a living tree, it must have gone through one half-life of decay. Therefore, we can estimate its age by multiplying the half-life by 1:
5730 years (half-life) x 1 = 5730 years
Therefore, the approximate age of the ancient wood is 5730 years. However, this is only an approximation and more accurate dating methods may be needed to determine the exact age of the wood.
8. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 10 g sample of radon-222 would be left after 15.2 days?
To solve this problem, we need to determine how many half-lives have passed in 15.2 days:
15.2 days รท 3.8 days/half-life = 4 half-lives
So after 4 half-lives, the amount of radon-222 remaining can be calculated using the half-life equation:
Final amount = (Initial amount) x (1/2)^(number of half-lives)
Final amount = 10 g x (1/2)^4
Final amount = 10 g x 0.0625
Final amount = 0.625 g
Therefore, after 15.2 days, only 0.625 g of the original 10 g sample of radon-222 would be left.
To determine the approximate age of the ancient wood, we can use the concept of half-life.
The half-life of carbon-14 is known to be 5730 years. This means that after 5730 years, half of the carbon-14 in a sample will have decayed.
In this case, we know that the ancient wood contains only half as much carbon-14 as a piece of wood from a living tree. This indicates that the ancient wood has undergone one half-life of decay.
Given that one half-life is 5730 years, we can conclude that the approximate age of the ancient wood is 5730 years.