100g of bone contain ratio of 14C and 12C. 6.8% 14C is present in the living tissue, how old was the skeleton? [for 14C, half-life is 5.73x10^3 years]
please help me choose an equation for this type of question.
What are you assumptions of the initial ratio of c14/c12 in the tissue?
Yes, oddly worded question.
To determine the age of the skeleton based on the ratio of 14C and 12C, you can use the formula for exponential decay. The equation for exponential decay is given by:
N(t) = N0 * e^(-λt)
Where:
N(t) = the amount of the isotope remaining at time t
N0 = the initial amount of the isotope
e = the mathematical constant approximately equal to 2.71828
λ = the decay constant (related to the half-life of the isotope)
t = time passed since the death of the organism
In this case, you have 6.8% of the 14C remaining, and you want to find the age of the skeleton. Since the half-life of 14C is known as 5.73x10^3 years, you can calculate the decay constant (λ) using the formula:
λ = ln(2) / half-life
Plugging in the values:
λ = ln(2) / 5.73x10^3 years
Once you have the decay constant (λ), you can rearrange the exponential decay equation to solve for time (t):
t = (-ln(N(t) / N0)) / λ
In this case, N(t) is 6.8% of the initial amount (N0) of 14C. So plug in 0.068 for N(t) and 1.00 for N0, and solve for t.
Keep in mind that this method assumes a constant atmospheric level of 14C and that the ratio of 14C to 12C is the same in living tissue as it is in the atmosphere.