When an unstable nucleus emits
a neutron, by how much does the mass number of the nucleus change?
So in this example, we have an
unstable atomic nucleus. We can show that here, with the
blue circles representing positively charged protons and the green circles
representing neutrally charged neutrons. And our problem statement tells
us that this nucleus is unstable and emits a neutron. So we could represent that this
way, with our nucleus giving off a green circle, a neutron. And the question is, how much
does this emission change the mass number of the nucleus?
Well, let’s remind ourselves
what the mass number of any given nucleus is. Say that we have some atomic
element. We don’t know what element it
is, so we’ll just give it the symbol X to represent that element. We know this element has some
number of protons in its nucleus. We represent that with Z, which
stands for the atomic number of the element. And if we add together the
number of protons with the number of neutrons in its nucleus, we get what’s
called its mass number. So Z, the atomic number, is the
number of protons in the nucleus. And N, the mass number, is the
number of protons plus the number of neutrons.
All this to say, if we were
interested in solving for the number of neutrons in an atom, we could subtract
Z, the atomic number, from N, the mass number. But anyway, for our purposes,
we don’t want to know about the number of neutrons in the nucleus. But rather, how much does the
mass number of the nucleus change. And this change, as we saw,
happens as a result of neutron emission.
Now, since the mass number of
any nucleus, including the unstable nucleus we have here, is equal to the number
of protons plus the number of neutrons in the nucleus. That means if we subtract away
a neutron — as a result of neutron emission, like we did here — then that mass
number will decrease by one. That’s because we’ve kept the
same number of protons, but we’ve lost a neutron. And that, then, is our answer
to this question. When an unstable nucleus emits
a neutron, its mass number decreases by one.