Video Transcript
The following nuclear equation
shows how an isotope of curium decays to plutonium via alpha decay. What are the values of 𝑝 and 𝑞 in
the equation?
Taking a look at this equation, we
see that curium, symbolized Cm, is decaying into plutonium, Pu, plus an alpha
particle, symbolized with the Greek letter 𝛼. This decay event means that the
curium nuclei has become unstable. And it’s split up into two pieces,
the plutonium plus the alpha particle. We see that, for curium as well as
for plutonium, both the atomic number as well as the mass number is given. But for the alpha particle, instead
of those numbers, we have a 𝑞 and a 𝑝, respectively. It’s those values we want to solve
for. And as we’ll see, there are two
ways of going about doing this.
The first way is to recall what an
alpha particle is, what it consists of. An alpha particle, the particle
emitted in an alpha decay event, consists of two protons as well as two
neutrons. That means if we were to represent
an alpha particle as though it was its own atomic element, we would write its atomic
number, the number of protons it has, two, and then its mass number, the sum of
protons as well as neutrons in the particle, four. These numbers are true for any
alpha particle. They always have two protons and
two neutrons.
The alpha particle involved in this
equation is the same way. It also has two protons and two
neutrons. This will indicate to us that 𝑞 is
equal to two and that 𝑝 is equal to four. This is one way to find the answer
to this question. But as we’ll see, there’s another
way, even if we didn’t recall this about an alpha particle.
This second approach involves
looking at these values, 𝑝 and 𝑞, in terms of the equation that they’re part
of. This type of nuclear decay
equation, where one kind of element decays into another element plus an alpha
particle, involves what we could call the conservation of atomic number — that’s
this number here to the lower left — as well as the conservation of mass number —
that’s this number here to the upper left. In other words, the atomic number
and the mass number on the left of this equation equal the sum of the atomic numbers
and mass numbers on the right of the equation. This means there are two separate
equations we can write down to help us solve for 𝑝 and 𝑞.
First, we can write down the atomic
number equation. Since atomic number is conserved
across this equation, it means that 96, the atomic number of curium, is equal to 94,
the atomic number of plutonium, plus the atomic number of the alpha particle. That’s 𝑞. And then, likewise, for the mass
numbers of these constituents, the mass number of curium, 247, is equal to the mass
number of plutonium, 243, plus the mass number of the alpha particle, 𝑝. We can use these two separate
equations to solve for 𝑞 and to solve for 𝑝. 𝑞 is equal to 96 minus 94, or
two. And 𝑝 is equal to 247 minus 243,
or four. Whichever of these approaches we
use, we end up finding that 𝑝 is equal to four and 𝑞 is equal to two.
