# Homework Help: Proportion of atmospheric Carbon 14

1. Apr 29, 2007

### poiuy

The half-life of Carbon 14 is 5730 years and the activity of atmospheric carbon due to Carbon 14 is 255Bq/Kg. What proportion of atmospheric carbon atoms are Carbon 14.

Attempted solution

Decay constant for C14 = ln(2)/t(1/2) = ln(2)/5730 = 1.21x10^-4

Current activity A = A(0)exp(-1.21*10^-4 *t )
A = 255
t = age of universe = 10*10^9 years

After this I start getting silly numbers and it just doesn't work, presumably A/A(0) would give the proportion of the current atmosphere which is C14, but then again this doesn't seem to work and I am all out of ideas.

All ideas appreciated (I don't really want the answer but if somebody could point me in the right direction that would be great)

2. Apr 30, 2007

### denverdoc

This might be better posted on the chemistry, other sciences, forum for homework help.

My first blush impression is that you need to be using the same units, in one case you're given the measured breakdown per second, and comparing it to a rate constant given in years. I don't believe that the age of the universe enters it. Instead, you have a number of events/sec, from the half life should be able to predict number of events on normalized basis, the fraction should give some idea about the percentage.

In other words say we have 1,000,000 carbon 14 atoms per kg.
In 5730 years, we would expect 500,000 to decay. In a second we would expect how many to decay? We know we have 255. That proportion of actual/expected is proportional to a million. What I dont understand is if its a Kg of atmosphere or Kg of carbon 14 thats being cited.

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