00:01
In this problem we're going to be looking at decay of 232, 90 thorium.
00:06
Now before we go on let's talk about notation and then about the actual decay processes that take place.
00:16
So just representing any element x, the superscript a is called the mass number, is equal to n plus c, the number of neutrons plus the number of protons.
00:36
The subscript c is called the atomic number.
00:44
You might say well okay that's the number of protons but it actually has a more general purpose that is not contradictory but it also can be thought of as the charge in units of e on the object as you'll see when i write out the decay process i'll explain that more there.
01:04
So let's look at alpha decay.
01:10
Because of the decay of the thorium we're going to see beta decay and alpha decay.
01:16
But alpha particle is just a helium nucleus, that's all it is.
01:25
So if you start out with azx you end up with a minus 4, c minus 2, y plus and here's the helium nucleus 4, 2, he.
01:39
I say how'd you know that? well because in nuclear decays the mass number is conserved on the left and on the right and the charge is always conserved no matter what process.
01:56
So a minus 4 plus 4 is a, c minus 2 plus 2 is z.
02:00
That's how they're conserved.
02:02
So that's how we know that.
02:04
So that's alpha decay.
02:06
Notice in alpha decay both a and z change.
02:10
I say that because of what's coming next.
02:13
Let's talk about beta minus decay.
02:14
That's what's involved here.
02:18
This is a beta minus particle is an electron.
02:21
There are beta plus particles, those are called positrons, they're positively charged.
02:26
We will not be dealing with beta plus decay here, we'll be dealing with beta minus decay.
02:32
So in this case azx goes to a, c plus 1, y plus the beta particle, the electron.
02:44
Notice notation, but let me finish it off.
02:47
Plus 0, 0, this is an anti -electron neutrino.
02:55
So let's look at the conservation laws.
02:57
A plus 0 plus 0 is a.
02:59
Good.
03:00
C plus 1 minus 1 plus 0, c.
03:03
So everything's fine there.
03:05
But as i mentioned, this top number is really the number of nucleons in that object.
03:11
Well electrons are not nucleon, it's not made up of nucleons.
03:16
So it has 0 for that.
03:19
N is 0 and z is 0 for that.
03:22
Now if you talk about, like i said, you talk about the charge, not the number of protons, but you think of this bottom number as the charge in units of e.
03:31
What's a proton? 1e.
03:32
What's an electron? minus 1e.
03:37
So that's, in general, it's a better way of thinking it that way, even though it can be, you know, having a z of 10, 10e, means you have 10 protons.
03:49
So it's, like i said, they're not contradictory ideas, but they are, one has greater utility in general than the other.
04:02
And that's thinking of it as a charge.
04:05
So this is the electron.
04:07
But when we're talking about decay, we usually write beta.
04:11
Some don't even put these on here.
04:12
They'll just write beta minus.
04:15
It depends on the book and the professor and so on.
04:19
Okay, but really what's going on here? that's really what's going on is in the beta minus decay is what is called neutron conversion.
04:28
Notice the number of nucleons does not change, though the number of protons went up by 1.
04:35
That means we had to lose a neutron.
04:38
That neutron was converted to a proton and electron.
04:41
Let me write it out.
04:42
This is the base process that takes place in the nucleus.
04:46
Here is a neutron, has no charge, and it is, it's a neutron, it's a nucleon.
04:54
It's made up of one, that object's made up of one nucleon, in this case a neutron.
05:03
One, one p, there's the proton, charge one e, and it's a proton.
05:09
So there's one, it's made up, that object is made up of one nucleon, one proton.
05:13
Z is one.
05:15
Plus zero, minus one e, plus zero, zero.
05:23
There's the actual neutron conversion.
05:26
That's what takes place.
05:28
These, the electron and the electron antineutrino are expelled quickly from the nucleus.
05:33
Obviously the proton does not go.
05:34
It's still there.
05:37
Okay, so those are the two processes.
05:40
So remember with alpha decay, a goes down by four, z goes down by two.
05:44
Beta decay, a is unchanged, and you increase z value by one.
05:52
Okay, now let's talk about the initial process.
05:57
The diagram they give you picks it up after the initial decay.
06:02
They say that in words, at the initial thorium decay, the first, that's actually really the daughter decay series, what they're actually doing there.
06:14
So they wrote the words, they put thorium in that first box.
06:17
Really that shouldn't, as we're going to see, this should be, that really is radium is sitting there.
06:26
But they put in words after the alpha decay of thorium, the daughter decays and such.
06:33
So read it very carefully...