The half life of carbon 14 is 5730 years. If the original amount in a particular living organism is 20g and that found in a fossil is 0.01g, determine the actual age of the fossil.
To determine the actual age of the fossil with the given information, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t / half-life)
Where:
N(t) = the remaining amount of carbon-14 at time t
N0 = the original amount of carbon-14
t = time elapsed
half-life = time it takes for half of the material to decay
In this case, the original amount of carbon-14 is 20g, and the remaining amount in the fossil is 0.01g. We need to determine the time, t.
0.01 = 20 * (1/2)^(t / 5730)
Divide both sides of the equation by 20:
0.0005 = (1/2)^(t / 5730)
To solve for t, we can take the logarithm of both sides:
log(0.0005) = log((1/2)^(t / 5730))
Using the logarithm property, we can bring the exponent down:
log(0.0005) = (t / 5730) * log(1/2)
Now we can solve for t by dividing both sides by log(1/2):
t / 5730 = log(0.0005) / log(1/2)
t = (log(0.0005) / log(1/2)) * 5730
Using a calculator, we can compute the value of t:
t ≈ 30188.49
Therefore, the actual age of the fossil is approximately 30188.49 years.
Age of fossil = (5730 x ln(20/0.01))/ln(2)
= (5730 x 4.60517018598809)/0.693147180559945
= 801,945.9 years