Video Transcript
The following nuclear equation
shows the fission of uranium-235 into xenon and strontium. We can see that uranium-235 is
decaying into xenon-140 and strontium-94, as well as some neutrons. How many neutrons are produced in
this reaction?
So basically, having seen this
nuclear reaction, we need to try and work out how many neutrons there are over
here. And the way to do this is to
remember that a correct nuclear equation will be based on the principles of
conservation of mass number. Now, what the conservation of mass
number tells us is that the total mass number before a reaction is equal to the
total mass number after the reaction. And this of course applies to the
reaction that we’re considering here. But then what do we even mean by
mass number?
Well, we can recall that the mass
number of an entity is equal to the total number of protons and neutrons in that
entity. So for example, if we just think of
the uranium nucleus that we started with, then the mass number of this uranium
nucleus is the total number of protons and neutrons in that nucleus. Now, the mass number for a nucleus
in its chemical symbol is traditionally given in the top left-hand corner of that
nucleus chemical symbol.
So for this uranium nucleus, we see
that the mass number is 235. In other words then, we see that
the total number of protons and neutrons in this uranium nucleus is 235. And actually, because we only have
the uranium nucleus before the reaction happens, the total mass number before the
reaction must be 235 because there’s nothing else on the left-hand side of the
equation. And so using a conservation of mass
number, we can say that 235, the total number of protons and neutrons before the
reaction or on the left-hand side, is equal to the total number of protons and
neutrons on the right which must be equal to 140, which is the mass number of xenon,
plus 94, which is the mass number of strontium, plus the number of neutrons that are
released.
And so in the equation that we’re
creating, we’ll say that 235 is equal to 140 plus 94 plus 𝑥 which is what we call
the number of neutrons produced. Now, it’s important to note that
the nuclear equation is telling us that this particular xenon nucleus has 140
protons and neutrons in total. This particular strontium nucleus
has 94 protons and neutrons in total. And only neutrons are produced
apart from this. In other words, no protons are
produced or no other nuclei are produced. And so the conservation of mass
number must apply to everything on the right-hand side that’s been given to us.
And since neutrons do form part of
mass number, remember mass number is total number of protons and neutrons, we can
therefore use this to calculate the number of neutrons, which we’re calling 𝑥. So all we need to do to calculate
𝑥 then is to rearrange this equation at the bottom. We simply need to subtract 140 and
94 from both sides of the equation because, this way, the 140 and minus 140
cancel. And same is true for 94 minus
94. So on the right, we’re just left
with 𝑥. And on the left, we’ve got negative
140 minus 94 plus 235. So evaluating the expression on the
left, we find that one is equal to 𝑥. In other words then, the total
number of neutrons produced in this reaction is one.
