Radioactive dating sample problems

So anyway, we have our atmosphere, and then coming from our sun, we have what's commonly called cosmic rays, but they're actually not rays. You can view them as just single protons, which is the same thing as a hydrogen nucleus. They can also be alpha particles, which is the same thing as a helium nucleus.

Carbon 14 dating 1

And there's even a few electrons. And they're going to come in, and they're going to bump into things in our atmosphere, and they're actually going to form neutrons. So they're actually going to form neutrons. And we'll show a neutron with a lowercase n, and a 1 for its mass number. And we don't write anything, because it has no protons down here. Like we had for nitrogen, we had seven protons. So it's not really an element. It is a subatomic particle. But you have these neutrons form.

And every now and then-- and let's just be clear-- this isn't like a typical reaction. But every now and then one of those neutrons will bump into one of the nitrogen's in just the right way so that it bumps off one of the protons in the nitrogen and essentially replaces that proton with itself.

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So let me make it clear. So it bumps off one of the protons. So instead of seven protons we now have six protons. But this number 14 doesn't go down to 13 because it replaces it with itself. So this still stays at And now since it only has six protons, this is no longer nitrogen, by definition. This is now carbon.

And that proton that was bumped off just kind of gets emitted. So then let me just do that in another color. And a proton that's just flying around, you could call that hydrogen 1. And it can gain an electron some ways. If it doesn't gain an electron, it's just a hydrogen ion, a positive ion, either way, or a hydrogen nucleus.

Radioactive dating example problems

But this process-- and once again, it's not a typical process, but it happens every now and then-- this is how carbon forms. So this right here is carbon You can essentially view it as a nitrogen where one of the protons is replaced with a neutron.

Carbon-14 Radioactive Dating Worked Example - Doc Physics

And what's interesting about this is this is constantly being formed in our atmosphere, not in huge quantities, but in reasonable quantities. So let me write this down.

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And let me be very clear. Let's look at the periodic table over here. So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon So carbon is the most common. So most of the carbon in your body is carbon But what's interesting is that a small fraction of carbon forms, and then this carbon can then also combine with oxygen to form carbon dioxide.

And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. It can be fixed by plants. When people talk about carbon fixation, they're really talking about using mainly light energy from the sun to take gaseous carbon and turn it into actual kind of organic tissue. And so this carbon, it's constantly being formed. It makes its way into oceans-- it's already in the air, but it completely mixes through the whole atmosphere-- and the air.

And then it makes its way into plants. And plants are really just made out of that fixed carbon, that carbon that was taken in gaseous form and put into, I guess you could say, into kind of a solid form, put it into a living form. That's what wood pretty much is. It gets put into plants, and then it gets put into the things that eat the plants. So that could be us. Now why is this even interesting?

Half-life and carbon dating (video) | Nuclei | Khan Academy

I've just explained a mechanism where some of our body, even though carbon is the most common isotope, some of our body, while we're living, gets made up of this carbon thing. Well, the interesting thing is the only time you can take in this carbon is while you're alive, while you're eating new things. Because as soon as you die and you get buried under the ground, there's no way for the carbon to become part of your tissue anymore because you're not eating anything with new carbon And what's interesting here is once you die, you're not going to get any new carbon And that carbon that you did have at you're death is going to decay via beta decay-- and we learned about this-- back into nitrogen So kind of this process reverses. So it'll decay back into nitrogen, and in beta decay you emit an electron and an electron anti-neutrino. Calculations of the binding energy can be simplified by using the following conversion factor between the mass defect in atomic mass units and the binding energy in million electron volts.

Calculate the binding energy of U if the mass of this nuclide is Click here to check your answer to Practice Problem 5. Click here to see a solution to Practice Problem 5. Binding energies gradually increase with atomic number, although they tend to level off near the end of the periodic table. A more useful quantity is obtained by dividing the binding energy for a nuclide by the total number of protons and neutrons it contains.

This quantity is known as the binding energy per nucleon. The binding energy per nucleon ranges from about 7. It reaches a maximum, however, at an atomic mass of about 60 amu. The largest binding energy per nucleon is observed for 56 Fe, which is the most stable nuclide in the periodic table. The graph of binding energy per nucleon versus atomic mass explains why energy is released when relatively small nuclei combine to form larger nuclei in fusion reactions. It also explains why energy is released when relatively heavy nuclei split apart in fission literally, "to split or cleave" reactions.

There are a number of small irregularities in the binding energy curve at the low end of the mass spectrum, as shown in the figure below. The 4 He nucleus, for example, is much more stable than its nearest neighbors. The unusual stability of the 4 He nucleus explains why -particle decay is usually much faster than the spontaneous fission of a nuclide into two large fragments.

Radioactive nuclei decay by first-order kinetics. The rate of radioactive decay is therefore the product of a rate constant k times the number of atoms of the isotope in the sample N. The rate of radioactive decay doesn't depend on the chemical state of the isotope. The rate of decay of U, for example, is exactly the same in uranium metal and uranium hexafluoride, or any other compound of this element. The rate at which a radioactive isotope decays is called the activity of the isotope. The most common unit of activity is the curie Ci , which was originally defined as the number of disintegrations per second in 1 gram of Ra.

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  5. The curie is now defined as the amount of radioactive isotope necessary to achieve an activity of 3. The most abundant isotope of uranium is U; Calculate the activity of the U in 1 L of a 1. Assume that the rate constant for the decay of this isotope is 4. Click here to check your answer to Practice Problem 6.

    Click here to see a solution to Practice Problem 6. The relative rates at which radioactive nuclei decay can be expressed in terms of either the rate constants for the decay or the half-lives of the nuclei. We can conclude that 14 C decays more rapidly than U, for example, by noting that the rate constant for the decay of 14 C is much larger than that for U. We can reach the same conclusion by noting that the half-life for the decay of 14 C is much shorter than that for U.

    The half-life for the decay of a radioactive nuclide is the length of time it takes for exactly half of the nuclei in the sample to decay. In our discussion of the kinetics of chemical reactions, we concluded that the half-life of a first-order process is inversely proportional to the rate constant for this process. Click here to check your answer to Practice Problem 7.