When thorium-232 undergoes one alpha decay followed by one beta decay, the resulting isotope is blank. A) Radium-228. B) Actinium-228. C) Francium-228. D) Actinium-232. Or E) uranium-236.
Just for reference, I’m gonna put out the names for each of these isotopes. The superscript number to the left indicates the mass number for the isotope, while the letters are an element symbol that you can find on your periodic table to match to the element name.
Thorium-232 is an isotope of thorium. When we say that thorium-232 decays, we mean that atoms or ions of thorium-232 decay. This is a schematic of a thorium-232 atom. There’s a highly dense thorium nucleus in the middle surrounded by electrons. Thorium has atomic number 90, so there are 90 protons in the nucleus. The mass number 232 tells us how many protons and neutrons we have in the nucleus. So, we can take 90 away from 232 to give us 142 neutrons.
During an alpha decay, an atom or ion will emit the equivalent of a helium nucleus. An alpha particle is a high-energy combination of protons and neutrons emitted from a nucleus. So, let’s imagine we’re losing an alpha particle from our thorium-232 atom or ion. We’re going to be losing two protons. So, the atomic number of the resulting isotope is going to be 90 minus two. And we’re losing two protons and two neutrons. That’s four lost from the mass number. So, what we get out is an isotope with atomic number 88 and mass number 228. If we look up the element with atomic number 88 on our periodic table, we’ll see that it’s radium, with symbol Ra.
The next step is a beta decay. A beta particle is a high-energy electron produced from the nucleus itself. But nuclei don’t contain electrons. During a beta decay, a neutron decays into a proton, releasing this high energy electron as well as other particles. We only need to worry about the proton and the electron here. So, now, what we have to do is think about what would be produced when a radium-228 atom or ion decays through beta emission.
Well, firstly, we’re gaining a proton, so the atomic number of the final isotope must be one greater than 88. However, since we’re converting a neutron into a proton, the total number of neutrons and protons doesn’t change. So, the mass number doesn’t change. So, the isotope of the atom or ion we produce would have a mass number of 228 and an atomic number of 89. If we look on our periodic table, the element with atomic number 89 is actinium, with symbol Ac.
So, we’ve taken our thorium-232 atom or ion through one alpha decay and one beta decay. As with many nuclear processes, we ignore the charge; we simply focus on the identity of the nuclei. We don’t need to display our final answer with the atomic number. We just need the mass member because the element symbol does the same job as the atomic number, telling us that we have 89 protons in the nucleus. So, when thorium-232 undergoes one alpha decay followed by one beta decay, the resulting isotope is actinium-228.