# Carbon-14 in a dead animal

1. Jul 2, 2012

### Flavia

Im having trouble answering this question.

How long it takes for 80% of the carbon-14 to decay in an animal after it has died.
Carbon decays rate 0.012% per year.

So, my understanding is,

-(R = 0.00012 yr-1, t=1 yr)
R=Ro exp (-λt)
0.00012=Ro exp(-λ(1)) ---- (1)

-No = 0.8,
No=λRo
Ro=0.8/λ ------ (2)

To find λ, (2) into (1)

0.00012=0.8/λ exp(-λ(1))
∴ λ = 8.8 yrs-1

Now im stuck which equation i have to use to find the year?
Are my assumption above is correct?

2. Jul 2, 2012

### Staff: Mentor

R=Ro exp (-λt) is the activity of the sample (decays per time)
0.00012/yr is the relative activity (decays per atoms per year)
They have a different meaning.

If 0.00012 of the probe decays per year, after one year the number of radioactive atoms and the activity is 0.99988 of its original value:

0.99988=1 exp (-λt) with t=1year. Can you use this equation to find λ?

3. Jul 2, 2012

### Flavia

so i can just assume the Ro=100% although it is given No=80%?

4. Jul 3, 2012

λ = - ln (0.99988) [in units of inverse years]

Then solve e-λt = 0.2 for t using the above...

5. Jul 3, 2012

### Staff: Mentor

No this is not given. It is given that 20% remains, which means R=0.2 R0 and N=0.2 N0