Finding the activity of a carbon 14 sample

Bolter · Apr 20, 2020

Hi there

So I have had a go at this question but I'm not confident that I have done the last 2 parts of this question right?

Printed exam Question 13 with parts (a) to (e) on radioactive half-life, activity, a graph of activity against time, decay constant for C-14 with half-life 5570 years, and activity per gram of carbon-14.

Handwritten notes on ruled paper: definitions of radioactive half-life and activity, a sketch graph of activity in Bq against half-lives showing exponential decay, and calculations for the decay constant lambda and the activity of C-14 atoms.

Handwritten working for part e of a radioactive decay problem: A = A0 e^(-λt) rearranged to ln(A0/A) = λt, giving t = (ln(A0) - ln(A))/λ, then λ = 0.693/(5570 × 365 × 24 × 60) = 2.367... × 10^-10 min^-1, A0 = 10.144..., and t = 5.15 × 10^9 mins.

Can anyone please see if this is what you do to get the values?

Any help would be appreciated! Thanks

haruspex · Apr 20, 2020

Think again about how you calculate the number of C14 atoms in the 1g.

Bolter · Apr 21, 2020

haruspex said:

Think again about how you calculate the number of C14 atoms in the 1g.

Is this what I should get instead?

Handwritten working on lined paper: Number of C-14 atoms = 1/12 x 6x10^23 x 1/10^12, followed by = 5x10^10 atoms.

I don't know why I was using 14 as the molar mass of carbon-12

etotheipi · Apr 21, 2020

Bolter said:

I don't know why I was using 14 as the molar mass of carbon-12

That appears to be a good enough approximation considering the huge excess of carbon-12, good enough for the precision of my calculator, anyway!

If the proportions were less extreme, you'd need to perhaps consider using a weighted mean or else an algebraic expression of some sort for the relative masses.

Bolter · Apr 21, 2020

etotheipi said:

That appears to be a good enough approximation considering the huge excess of carbon-12, good enough for the precision of my calculator, anyway!

If the proportions were less extreme, you'd need to perhaps consider using a weighted mean or else an algebraic expression of some sort for the relative masses.

Thanks I understand, and notably this means my answer will be affected for part e) as part e) relies on part d)

I changed it now and found the time that the activity will reduce to 3 disintegrations per min assuming 11.835... is the initial activity in disintegrations per min

Handwritten calculation on lined paper: number of C-14 atoms = (1/12) x 6x10^23 x (1/10^12) = 5x10^10 atoms; A0 = (2.367...x10^-10)(5x10^10) = 11.835...; t = (ln(A0) - ln(3))/λ = (ln(11.835...) - ln(3))/(2.367...x10^-10); t = 5.80x10^9 mins.

Finding the activity of a carbon 14 sample

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