### Video Transcript

The nuclear equation, shown here,
shows how argon decays to potassium via beta decay. What is the value of π in the
equation?

Taking a look at this equation, we
see that, indeed, the element argon is decaying into potassium plus a beta
particle. Looking at the numbers
corresponding to each of these atomic symbols, we see that argon has 18 protons and
three nine protons plus neutrons. Going over to potassium, potassium
has π protons and 39 protons plus neutrons. Meanwhile, our beta particle,
symbolised over here, is an electron. Therefore, it has a charge of
negative one. And it has zero protons plus
neutrons.

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. That is, they have the same
magnitude, but the opposite sign. The charge of a proton is positive
while the charge of an electron is negative.

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. The total electric charge in this
reaction before the decay occurs must equal the total electric charge after the
decay occurs.

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. 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. We can simplify this. So it reads 18 yields π minus
one.

Since π minus one is equal to 18,
that must mean that π is equal to 19. Thatβs the number of protons in
potassium. And itβs the value of π in this
equation.