WEBVTT
00:00:00.200 --> 00:00:06.370
The nuclear equation, shown here, shows how argon decays to potassium via beta decay.
00:00:06.770 --> 00:00:09.080
What is the value of π in the equation?
00:00:09.450 --> 00:00:16.250
Taking a look at this equation, we see that, indeed, the element argon is decaying into potassium plus a beta particle.
00:00:16.580 --> 00:00:24.830
Looking at the numbers corresponding to each of these atomic symbols, we see that argon has 18 protons and three nine protons plus neutrons.
00:00:25.090 --> 00:00:30.690
Going over to potassium, potassium has π protons and 39 protons plus neutrons.
00:00:30.920 --> 00:00:34.950
Meanwhile, our beta particle, symbolised over here, is an electron.
00:00:35.220 --> 00:00:37.190
Therefore, it has a charge of negative one.
00:00:37.220 --> 00:00:39.480
And it has zero protons plus neutrons.
00:00:39.810 --> 00:00:48.100
When it comes to the charge on an electron, such as the charge of a beta particle and the charge of a proton, we know these charges are equal and opposite.
00:00:48.540 --> 00:00:51.660
That is, they have the same magnitude, but the opposite sign.
00:00:51.930 --> 00:00:55.420
The charge of a proton is positive while the charge of an electron is negative.
00:00:55.780 --> 00:01:07.490
When our question asks what the value of π is in the equation, where π is the number of protons and potassium, we can solve for this by realising that, across this nuclear equation, electric charge is conserved.
00:01:07.930 --> 00:01:15.150
The total electric charge in this reaction before the decay occurs must equal the total electric charge after the decay occurs.
00:01:15.410 --> 00:01:29.130
If we let positive one represent the charge of a proton and negative one represent the charge of an electron, then we can say that, initially, in this reaction, we have 18 times positive one electric charge, 18 protons.
00:01:29.420 --> 00:01:39.460
Then, after the decay event, we have π, an unknown number we want to solve for, plus one times negative one because thereβs one electron in the beta particle.
00:01:39.860 --> 00:01:41.090
We can simplify this.
00:01:41.090 --> 00:01:43.820
So it reads 18 yields π minus one.
00:01:44.120 --> 00:01:48.780
Since π minus one is equal to 18, that must mean that π is equal to 19.
00:01:49.090 --> 00:01:51.520
Thatβs the number of protons in potassium.
00:01:51.550 --> 00:01:53.640
And itβs the value of π in this equation.