A radiation detector in a labaratory records a reading of 10 counts / min. There are no radioactive samples in the laboratory. Carbon has a half life of 5700 years. There are atoms of carbon-14 in all living organisms. An archaeologist digs up some ancient wood gives a reading of 20 counts / min. Sn equivalent sample of living wood gives a rreading of 80 counts / min. Do a calculation to check whether this suggestion is correct.

The question seems to be asking whether the age of the ancient wood can be determined based on the given radioactive decay rates. To answer this, we can use the concept of half-life, which is the time it takes for half of the radioactive atoms in a sample to decay.

Here are the steps to solve this problem:

1. First, we need to correct the readings for background radiation. The background radiation is 10 counts/min, so we subtract this from the readings. The corrected reading for the ancient wood is 20 - 10 = 10 counts/min, and for the living wood is 80 - 10 = 70 counts/min.

2. Next, we calculate the ratio of the corrected readings of the ancient wood to the living wood. This gives us 10 / 70 = 0.143.

3. The half-life of carbon-14 is 5700 years. This means that after 5700 years, half of the carbon-14 in a sample will have decayed.

4. We can use the formula for radioactive decay, which is N = N0 * (1/2)^(t/T), where N is the final quantity, N0 is the initial quantity, t is the time, and T is the half-life.

5. In this case, we know that N/N0 = 0.143, and we're trying to find t. We can rearrange the formula to solve for t: t = T * log2(N0/N).

6. Substituting the given values into the formula gives us t = 5700 * log2(70/10) = 5700 * log2(7) = 5700 * 2.807 = 16,000 years.

So, the calculation suggests that the ancient wood is approximately 16,000 years old. This is a rough estimate, as the actual age could be slightly different due to factors such as variations in the carbon-14 concentration in the atmosphere over time.