14/6 c has a half-life of 5600 years. An anyalsis of charcoal from a wood fire shows that 14c content is 25 per cent of living wood.

how many years have passed since fire for the wood was cut

k = 0.693/t1/2

Substitute the value of k into the below equation.
ln(No/N) = kt
No = 100
N = 25
k from above
Solve for t in years.

Yes

To determine the number of years that have passed since the wood was cut for the fire, we can use the concept of half-life for carbon-14 (14C).

First, let's understand what half-life means. The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of 14C is given as 5600 years.

Given that the 14C content in the analyzed charcoal is 25% of its original content in living wood, we can deduce that the remaining 75% has decayed.

Now, we need to determine how many half-lives have passed to reach this decay percentage. We can use the formula:

(number of half-lives) x (half-life of substance) = time passed

Let's calculate the number of half-lives first:

75% (remaining 14C content) = 100% (initial 14C content) / 2^(number of half-lives)

Dividing both sides by 100% and multiplying by 2, we get:

0.75 = 0.5^(number of half-lives)

Now, take the logarithm (base 0.5) of both sides to solve for the number of half-lives:

log(0.75) = log(0.5^(number of half-lives))

Using logarithmic properties, we can rewrite the equation as:

log(0.75) = (number of half-lives) * log(0.5)

Solving for the number of half-lives:

(number of half-lives) = log(0.75) / log(0.5)

Using a calculator, we find that the number of half-lives is approximately 1.415.

Now we can calculate the time passed since the wood was cut:

time passed = (number of half-lives) x (half-life of 14C)

time passed = 1.415 * 5600 years

Finally, we can calculate the final answer:

time passed = 7916 years

Therefore, approximately 7916 years have passed since the wood was cut for the fire.