Petroleum is a fossil fuel containing many diffferent carbon compounds. If the carbon atoms in petroleum...?

Question

have been in the ground for 100 million years, what fraction of the initial C-14 atoms is still there? (t1/2 = 5,370 yrs)

a. 0
b. 1 x 10^[-]10
c. 5.7 x 10^[-]5
d. 1.0 x 10^[-]3
e. 5.7 x 10^[-]1

Not sure how to answer this. Could you please show me the steps in your result so that I'll have a greater understanding of the problem?? (TIA)

Answer 1

If n0 atoms of C-14 decays over a period of t with a rate constant of k, and after time t, n atoms of C-14 are still there, then, we know that: (it's a first order decay after all!)
n/n0=exp(-kt) ------(1)
=> k= [ln(n0/n)]/t --(2)
First solve for k by plugging in n/n0 = 1/2, and t = 5370 yr in Eq(2).
Then, plug in the value of k (that you calculated) and t = 100x10^6yr (100 million yrs) in Eq.1, and calculate n/n0 (the fraction).

Answer 2

It is actually a FACT that we are currently on the down cycle of a cyclical temperature fluctatuation. There are many models that show that, in less than 10000 years, the blink of an eye in historical measures, the entire eastern and western seaboards will be completely COVERED with glacial ice. Every single northern city area will be crushed to rubble, destroyed under hundreds and thousands of feet of solid ice. We should be rejoicing in the fact that we are actually contributing, even so slightly, less than 1%, towards the continuance of warmer temperatures, pushing that fate off maybe a few years. Just think of all the creatures that we are saving from extinction, potentially several generations, before the ice claims their habitats. During its hot phases, the earth has historically been a lot warmer than it is now. Prehistoric fossils show most of the planet covered with dense jungles and rain forests. And what is the life-giving food that they depend on for such growth? CO2. We know that there is recent evidence that parts of the Sahara are being reclaimed -- naturally -- by vegetation at its edges, all thanks to CO2. We should be thankful that parts of the arctic are melting. Just think of all the life that will finally be reborn in those areas, all the plants, all the animals, dormant for all these years, finally able to breathe into existence again. The cure for cancer and other disease may even wait under that ice, in some long-lost bacteria. Change is always a good thing. Nature provides change. Global warming is a natural cycle that precedes global cooling. It's sad when people give themselves pretentious godlike abilities to "control and affect the universe", when in fact our rather pathetic presence is considerably insignificant and far outshined by even the most microscopic organisms like bacteria. What's scary is that a religion based on that fantasy has taken hold worldwide, and that we're all being forced to drink their poisoned Kool-Aid, even if we disagree with the religion.

Answer 3

Since the numbers are pretty spread out, you can cheat a little by finding number of half-lives which would be 10^8 divided by 5370. which is about 1.9x10^4. Very roughly, 20 half-lives corresponds to a fraction of 1x10^-6 (one in one million). Since you have so many more here, the answer would be essentially zero.

Answer 4

Use the exponential function. You know the half life. So you know the time constant tau after which the remaining number of atoms is 1/e of the original number. Now you calculate the natural logarithm (logarithm to base e) of the fraction. That is the number you have to multiply the tau with to the correct number of years. Easy.