Help with carbon dating question please

[cd95]

desperately need help with the question below. me and my dad have been working on it for hours but keep getting the answer to be 5.97x10^-23?! totally off what it should be.

Q. There are about 1.3x10^-12 carbon-14 atoms for each atom of carbon-12 in living materials, and the half-life of carbon-14 is 5730 years. Show that the number of disintegrations occurring in 1 mole of carbon from a living organism is 2.3 per second.

Thanks

Charley

 

[ehild]

Show what you and your dad have done so far. What do you know about radioactive decay? What is half-life?

ehild

 

[cd95]

this is what we worked out...

(1.3x10^-12) x 12 = 1.56x10^-11 gm C14/gm C

then using the equation Kb=ln2/half-life...

Kb=ln2/(1.80x10^11) seconds = 3.85x10^-12 disintegrations per second

Then...
(3.85x10^-12) x (1.56x10^-11) = 5.97x10^-23

what have we missed?

 

[SteamKing]

How many atoms are in one mole of a substance? Remember, it is the number of disintegrations of individual atoms that you are looking for.

 

[paranormal]

Hello Charley,

I understand your frustration with this question, but let's break it down step by step to see where the error may be occurring.

First, let's remember that carbon-14 is a radioactive isotope of carbon that decays over time. This decay process is measured using the concept of half-life, which is the amount of time it takes for half of the original amount of a substance to decay.

In this question, we are given the information that there are 1.3x10^-12 carbon-14 atoms for each atom of carbon-12 in living materials. This means that for every 1.3x10^-12 grams of carbon-12 in a living organism, there is also 1.3x10^-12 grams of carbon-14. This ratio remains constant in living organisms.

Next, we are told that the half-life of carbon-14 is 5730 years. This means that after 5730 years, half of the original amount of carbon-14 will have decayed. After another 5730 years, half of that remaining amount will have decayed, and so on.

Now, to find the number of disintegrations occurring in 1 mole of carbon from a living organism, we need to use the Avogadro's number, which is 6.022x10^23. This number represents the number of particles (atoms or molecules) in one mole of a substance.

To find the number of disintegrations, we can use the formula N = N0 * (1/2)^(t/T), where N is the current number of atoms, N0 is the original number of atoms, t is the time, and T is the half-life.

Plugging in the given values, we get:

N = (1.3x10^-12 * 6.022x10^23) * (1/2)^(1/5730)

N = 7.84x10^11 * (1/2)^0.000114

N = 7.84x10^11 * 0.999886

N = 7.839x10^11

This means that for every mole of carbon in a living organism, there are approximately 7.839x10^11 disintegrations occurring per second.

I hope this explanation helps and clears up any confusion. Keep up the good work with your dad! Science can be challenging, but