Calculating Atomic Fraction of C in Carbon Dioxide at STP

[iamalexalright]

Homework Statement

In a sample of one litre of carbon dioxide at STP an average of 5 disintegrations

C -> N + e + v

are observed per minute. Calculate the atomic fraction of C present if the mean lifetime of this nucleus is 8267 years.

Homework Equations

$$\tau$$ = $$\omega$$^-1 = 8267 years

N(t) = N₀ * $$e$$^{-$$(\omega$$ * t)}

The Attempt at a Solution

First I found $$\tau$$ = 2.607 * 10¹¹ seconds.

And really I'm at a loss of where to go next. I figure N(t)/N₀ is what I am looking for but I cannot solve for this without knowing the time t and I do not know where the 5 disintegrations per minute comes in. I'm not looking for an answer(already know it), i just want a little push in the right direction.

 

[gabbagabbahey]

Homework Statement

In a sample of one litre of carbon dioxide at STP an average of 5 disintegrations

C -> N + e + v

are observed per minute. Calculate the atomic fraction of C present if the mean lifetime of this nucleus is 8267 years.

Homework Equations

$$\tau$$ = $$\omega$$^-1 = 8267 years

N(t) = N₀ * $$e$$^{-$$(\omega$$ * t)}

The Attempt at a Solution

First I found $$\tau$$ = 2.607 * 10¹¹ seconds.

And really I'm at a loss of where to go next. I figure N(t)/N₀ is what I am looking for but I cannot solve for this without knowing the time t and I do not know where the 5 disintegrations per minute comes in. I'm not looking for an answer(already know it), i just want a little push in the right direction.

Since there are an average of 5 disintegrations per minute, you would expect:

$$N(t)-N(t+60s)=5$$...can you take it from there?

 

[Astronuc]

Homework Statement

In a sample of one litre of carbon dioxide at STP an average of 5 disintegrations

C -> N + e + v

are observed per minute. Calculate the atomic fraction of C present if the mean lifetime of this nucleus is 8267 years.

Homework Equations

$$\tau$$ = $$\omega$$^-1 = 8267 years

N(t) = N₀ * $$e$$^{-$$(\omega$$ * t)}

The Attempt at a Solution

First I found $$\tau$$ = 2.607 * 10¹¹ seconds.

And really I'm at a loss of where to go next. I figure N(t)/N₀ is what I am looking for but I cannot solve for this without knowing the time t and I do not know where the 5 disintegrations per minute comes in. I'm not looking for an answer(already know it), i just want a little push in the right direction.

One can find the total amount of carbon from "one litre of carbon dioxide" - simply find the moles of CO₂ in 1 liter at STP. It would appear that one is to find the atomic fraction of radiocarbon or C-14.

The activity, decays per unit time, is the product of the decay constant $\lambda$ and the number of atoms of the radionuclide present, i.e. A(t) = $\lambda$ N(t). One is given A, so find N.