Question

In the carbon dating process for measuring the age of objects, carbon-14, a radioactive isotope, decays into carbon-12 with a half-life of 5730 years A Cro-Magnon cave painting was found in a cave in Europe. If the level of carbon-14 radioactivity in charcoal in the cave is approximately 11% of the level of living wood, estimate how long ago the cave paintings were made.

Answer 1

The cave paintings were made approximately 11,460 years ago based on the level of carbon-14 radioactivity in the charcoal compared to living wood.

Step-by-step explanation:

In the carbon dating process, the level of carbon-14 radioactivity in a sample is compared to the level of carbon-14 in living wood to estimate the age of objects. Carbon-14 has a half-life of 5730 years, meaning that half of the carbon-14 atoms in a sample will decay into carbon-12 over that time period. In this case, if the level of carbon-14 radioactivity in the charcoal is approximately 11% of the level in living wood, we can calculate the number of half-lives that have passed to determine the age of the cave paintings.

Since the level of carbon-14 radioactivity is 11% of the level in living wood, it means that the remaining carbon-14 is 89% of the original level. To find the number of half-lives, we can divide 89% by 50% (half of 100%) and round the answer to the nearest whole number. In this case, the number of half-lives is 2.

Since each half-life is 5730 years, we can multiply the number of half-lives (2) by the length of a half-life (5730 years) to estimate that the cave paintings were made approximately 11,460 years ago.

Answer 2

The carbon-14 level in the charcoal from the Cro-Magnon cave painting is about 11% that of living wood, indicating that the painting is roughly 18,000 years old.

Step-by-step explanation:

Radio Carbon Dating is a method used to determine the age of ancient objects by analyzing the levels of carbon-14 in them. Carbon-14 is a radioactive isotope that decays into carbon-12, and it has a half-life of 5730 years. When a living organism dies, the level of carbon-14 starts to decay and is not replenished. By measuring the remaining amount of carbon-14 in the sample and comparing it with the expected level in a living organism, we can estimate the time that has passed since death. For the Cro-Magnon cave painting, if the level of carbon-14 in the charcoal is approximately 11% of the level of living wood, we need to calculate the number of half-lives that have passed and then multiply this by the half-life of carbon-14 to estimate the age of the painting.

First, we find the decay factor, which is the current percentage of carbon-14 relative to that of a living organism. The decay factor here is 0.11 (representing 11%). To determine the number of half-lives that have passed, we use the formula:

Number of half-lives = - (log(current ratio) / log(2))

Plugging in the numbers:

Number of half-lives = - (log(0.11) / log(2))

Calculating this, we find that approximately 3.14 half-lives have elapsed since the wood was part of a living organism. Multiplying this value by the half-life of carbon-14:

Time elapsed = Number of half-lives * half-life of carbon-14

Time elapsed = 3.14 * 5730 years

We calculate that the time elapsed is approximately 18,000 years. Thus, the cave paintings were likely created about 18,000 years ago.