Question Video: Understanding Neutron Emission Physics

When an unstable nucleus emits a neutron, by how much does the mass number of the nucleus change?

01:54

Video Transcript

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.