Quiz on carbon dating
What I want to do in this video is kind of introduce you to the idea of, one, how carbon-14 comes about, and how it gets into all living things. They can also be alpha particles, which is the same thing as a helium nucleus. 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. And we'll show a neutron with a lowercase n, and a 1 for its mass number. And what's interesting about this is this is constantly being formed in our atmosphere, not in huge quantities, but in reasonable quantities. Because as soon as you die and you get buried under the ground, there's no way for the carbon-14 to become part of your tissue anymore because you're not eating anything with new carbon-14.
And then either later in this video or in future videos we'll talk about how it's actually used to date things, how we use it actually figure out that that bone is 12,000 years old, or that person died 18,000 years ago, whatever it might be. So let me just draw the surface of the Earth like that. So then you have the Earth's atmosphere right over here. And 78%, the most abundant element in our atmosphere is nitrogen. And we don't write anything, because it has no protons down here. And what's interesting here is once you die, you're not going to get any new carbon-14. You can't just say all the carbon-14's on the left are going to decay and all the carbon-14's on the right aren't going to decay in that 5,730 years.
Since we know the time and the amounts, we can calculate the constant k.
N(5730) = [N(0)e^(k*5730)] Since after 5730 years, 1/2 will remain, then N(t) = N(0)/2.
In 1991, hikers in the Tyrolean Alps of Europe made a remarkable discovery.1) The decay formula is N(t) = N(0)e^kt where: N(t) = amount of carbon 14 remaining after t years N(0) = initial amount of carbon 14 k = decay constant t = time in years Unfortunately problem 1 has two unkowns; k and t.However, the half-life of carbon 14 is known to be approximately 5730 years.Only round off the final answers.) Now that we know k, we can calculate the carbon 14 decimal amount remaining after 5300 years. N(t) = N(0)e^kt N(5300) = N(0)e^kt since we are dealing with percentages, we know that 100% is the original amount, and that is decimal 1.0. N(5300) = (1.0) * e^(-0.000120968 * 5300) N(5300) = e^(-0.000120968 * 5300) N(5300) = e^(-0.6411309) N(5300) = e^(-0.6411309) N(5300) = 0.526696446 = 52.67% remaining 2) N(t) = N(0)e^kt Since 5.5% = 0.055 in decimal, then N(t) = (0.055)N(0).(0.055)N(0) = N(0)e^(-0.000120968 * t) cancel out the N(0) on both sides and replace with 1's (0.055) * 1 = 1 * e^(-0.000120968 * t) 0.055 = e^(-0.000120968 * t) take natural log of both sides ln(0.055) = ln(e^(-0.000120968 * t)) -2.900422094 = -0.000120968 * t t = 23976.75279 = 23,977 years ago 3) Since we know that 8% of the carbon has been lost, then 92% remains (100 - 8 = 92).
N(0)/2 = N(0)e^(k*5730) cancel out the N(0)'s on both side and replace with 1's.