Carbon dating problems calculus
So if we say, the difference or change in our number of particles, or the amount of particles, in any very small period of time, what's this going to be dependent on?This is the number particles we have in a given period time. So one thing, we know that our rate of change is going down. We know that, in the case of radioactive decay, I could do the same exercise with compounding growth, where I would say, oh no, it's not a negative number, that our growth is dependent on how much we have.
So let's just think a little bit about the rate of change, or the probability, or the number particles that are changing at any given time.And so this would involve two half lives, which is the same thing as 2 times 5,730 years. You'd say this thing is 11,460 years old, give or take.SAL: The notion of a half-life is useful, if we're dealing with increments of time that are multiples of a half-life.If a fossil contains 60% of its original carbon, how old is the fossil? That means this is how long it takes for half the nuclei to decay.After 5600 years, if we start with a gram, we end up with half a gram.For example, where time equals zero, we have 100% of our substance.
Then after time equals one half-life, we'd have 50% of our substance.
After one half life, it would have had 1/2 the carbon.
And then after another half life, half of that also turns into a nitrogen-14.
If you have a fossil, you can tell how old it is by the carbon 14 dating method.
This is a formula which helps you to date a fossil by its carbon.
You really wouldn't see that with carbon-14, but this is just for the sake of our intuition.