decay formula

[Guest]

Hello, can someone tell me how to work out Q c ?

3. The basis for dating archaeological finds is that there has been a constant proportion of atmospheric 14C. Atmospheric carbon exists as three forms - the stable isotopes 12C (which constitutes 98.89% of atmospheric carbon) and 13C (1.11%), and the radioactive form 14C, 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 14C within the soft tissues and skeletons begins to decline.

The half life of 14C 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.
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(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.

[Guest]

Hello, can someone tell me how to work out Q c ?

3. The basis for dating archaeological finds is that there has been a constant proportion of atmospheric 14C. Atmospheric carbon exists as three forms - the stable isotopes 12C (which constitutes 98.89% of atmospheric carbon) and 13C (1.11%), and the radioactive form 14C, 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 14C within the soft tissues and skeletons begins to decline.

The half life of 14C 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.9

(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.

Can we presume that you have already done (a) and (b)?

The "decay formula" given is [tex]N= N_0 2^{-t/5568}[/tex]. Taking the logarithm, base 10, gives [tex]log_{10}(N)= log_{10}(N_0 2^{-t/5568})= log_{10}(N_0)- \frac{t}{5568}log_{10}(2)[/tex].

Do you see that the graph of that is a straight line with variable t? The "intercept of the y-axis" is the value of [tex]log_{10}(N)[/tex] when t= 0. What is that? The "gradient" is, of course, coefficient of t. What is that?

[Guest]

Thanks I have done a but am struggling to figure out how to do b as well if you can help

[Guest]

The half life of 14C 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.[/quote]
"How old" asks for time, t. You need to solve [tex]N/N0= 3.00 x 10^{-11}= 2^{-t}/5568[/tex]

(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?

So now t= 55000. t/T= 55000/5568= 9.8779. [tex]2^{-9.87}= [/quote] what?