00:01
When we're dealing with half -lives, we'll have a rate of decays, which equals some initial rate times e to the minus lambda t.
00:08
And lambda here is going to be the natural logarithm of two divided by the half -life of a substance.
00:15
And so we're told for a particular form of charcoal, we have a half -life of 5 ,568 years.
00:25
All right.
00:25
And so if we look at what our decay constant is in those units, this should be about 1 .245 times 10 to the negative fourth, and then the units we can just write as inverse years.
00:43
So with that said, we want to use this information to date a couple of samples.
00:48
So our first sample, we have a rate, we'll call this r.
00:52
Or sorry, we're told for charcoal, r not is about, let's see, 15 .3 decays per gram.
01:03
So we can just write that as like decays, or sorry, decays per minute per gram.
01:09
So we can write that this way.
01:11
So we're told that a given rate for the dead sea scrolls is 12 decays per minute per gram.
01:18
So we want to figure out how old it is.
01:19
So what we'll do is just do r divided by r0 is equal to e to the minus lambda t.
01:26
And so t, and this goes for really any of these problems, is going to be negative 1 over lambda times the natural logarithm of r over r not.
01:36
So if we plug that in for our first equation, we'll have 12 divided by 15 .3.
01:48
We take the natural logarithm of that, multiplied by negative 1...