Hello, I am struggling to undertand how to start with this question mainly what goes where and then what to do from there?
For part a the formula is N=N0 × 2^-t/T.
So T = 5568
N0 = 3.00 × 10^-11% ?
How do I know what t is?
The basis for dating archaeological finds is that there has been a constant proportion of atmospheric 14^C. Atmospheric carbon exists as three forms - the stable isotopes 12^C (which constitutes 98.89% of atmospheric carbon) and 13^C (1.11%), and the radioactive form 14^C, which makes up 1.00 × 10^-10 % of the atmospheric carbon. The carbohydrate produced by plants, and consumed by plant- and meat-eaters, has approximately the same composition of the three isotopes of carbon as the atmosphere. But when a plant or animal dies it stops incorporating new carbon and the proportion of 14^C within the soft tissues and skeletons begins to decline.
The half life of 14^C is T = 5568 years, and the radioactive decay of 14C can be modelled using the formula N=N0 × 2^-t/T where t is time.
(a) How old is an archaeological find that has been shown to have 14C equivalent to 3.00 × 10^-11% of the total carbon? Give your answer to 2 sig. figs.
(b) The instruments used to determine the age of an archaeological find are accurate to the percentage of 14C reached after 55000 years. What is this percentage to 2 sig. figs?
(c) Given the decay formula, we should get a straight line by plotting log10N on the y-axis against t on the x-axis. If we were to do this, what would be the value of the intercept of the y-axis and what would the gradient be? Give the units in both cases.
For part a the formula is N=N0 × 2^-t/T.
So T = 5568
N0 = 3.00 × 10^-11% ?
How do I know what t is?
The basis for dating archaeological finds is that there has been a constant proportion of atmospheric 14^C. Atmospheric carbon exists as three forms - the stable isotopes 12^C (which constitutes 98.89% of atmospheric carbon) and 13^C (1.11%), and the radioactive form 14^C, which makes up 1.00 × 10^-10 % of the atmospheric carbon. The carbohydrate produced by plants, and consumed by plant- and meat-eaters, has approximately the same composition of the three isotopes of carbon as the atmosphere. But when a plant or animal dies it stops incorporating new carbon and the proportion of 14^C within the soft tissues and skeletons begins to decline.
The half life of 14^C is T = 5568 years, and the radioactive decay of 14C can be modelled using the formula N=N0 × 2^-t/T where t is time.
(a) How old is an archaeological find that has been shown to have 14C equivalent to 3.00 × 10^-11% of the total carbon? Give your answer to 2 sig. figs.
(b) The instruments used to determine the age of an archaeological find are accurate to the percentage of 14C reached after 55000 years. What is this percentage to 2 sig. figs?
(c) Given the decay formula, we should get a straight line by plotting log10N on the y-axis against t on the x-axis. If we were to do this, what would be the value of the intercept of the y-axis and what would the gradient be? Give the units in both cases.