Video: Solving Nuclear Equations Involving Alpha Decay

Uranium-234 decays via alpha decay to thorium-230. Thorium-230 then decays via alpha decay to radium-226. How many protons in total are ejected from a uranium nucleus that undergoes this process?

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Video Transcript

Uranium-234 decays via 𝛼 decay to thorium-230. Thorium-230 then decays via 𝛼 decay to radium-226. This is shown in the following nuclear equation. Uranium-234 decays to thorium-230 plus one 𝛼 particle. And then the next stage is radium-226 plus two 𝛼 particles. How many protons in total are ejected from a uranium nucleus that undergoes this process?

Okay, so before we answer that question, let’s take a good look at this nuclear equation. So we see that we’ve got a uranium nucleus which decays to thorium and an 𝛼 particle. But then in the question, we’ve been told that the thorium-230 then decays via 𝛼 decay to radium-226. So essentially, what’s happening is that when we have a thorium and an 𝛼 particle, the thorium then decays to radium and releases an 𝛼 particle. But then this 𝛼 particle from earlier is the reason why we have two 𝛼 particles at the end. In other words, one was released by the uranium nucleus. And the other one was released by the thorium nucleus.

Now in this part of the question, we need to consider the number of protons ejected by the uranium nucleus in this entire reaction. And we can recall that this lower number here is the number of protons in this particular nucleus. This number is also the defining feature of what element we’re talking about. In other words, any nucleus with 92 protons in it must be a uranium nucleus. Similarly, any nucleus with 90 protons in it must be thorium and so on and so forth. Now, what we have initially is a uranium nucleus which contains 92 protons.

So let’s imagine we’ve drawn 92 protons here. Now, as well as this, there are 234 minus 92 neutrons in this nucleus. And the reason for this is that this number is the total number of nucleons in the nucleus. And nucleons are protons and neutrons. In other words, there are 234 protons and neutrons in this particular nucleus. And so the number of neutrons in the nucleus by itself must be 234 minus 92 which, in other words, is 142.

So let’s imagine we’ve drawn 142 neutrons in this nucleus. Now, what happens in this nuclear reaction is that the nucleus that we’ve drawn here releases an 𝛼 particle which has two protons and two neutrons. And, therefore, the nucleus that remains is the thorium nucleus with two fewer protons. So that’s 90 protons now and two fewer neutrons as well. So that’s 140. So these are the products of the first part of the reaction.

But then this thorium nucleus that we have decays even further into radium. This means now that it only has 88 protons and 138 neutrons because, once again, it’s lost an 𝛼 particle that has two protons and two neutrons. And of course as well as this, we’ve got the 𝛼 particle from the previous part of the reaction. Hence, these are the final products of the reaction, a radium nucleus with 88 protons and 138 neutrons and two 𝛼 particles, each of which have two protons and two neutrons.

Now in the entire process, the uranium nucleus becomes thorium. And then the thorium becomes radium. And it does this by losing, altogether, two 𝛼 particles. Now, each 𝛼 particle has two protons. So that’s two protons here and two protons here. And, therefore, the uranium nucleus in total has lost four protons because that’s two plus two. And so our answer to this part of the question is that four protons in total are ejected from a uranium nucleus that undergoes this process.

So now that we’ve discussed protons, let’s consider nucleons. How many nucleons in total are ejected from a uranium nucleus that undergoes this process? Now, as we said already, this is the atomic number or the number of protons in this particular nucleus. And this is the total number of protons and neutrons or, in other words, nucleons. Now, the number itself is referred to as the mass number. But the important thing is that it tells us the number of nucleons in this nucleus here. Now, we’ve already seen that this nucleus becomes a thorium nucleus. And then the thorium decays to radium. And all in all, the net effect is that it’s lost two 𝛼 particles.

Now, we said earlier that these 𝛼 particles have four protons in them. But they also have four neutrons altogether. Therefore, the number of nucleons lost by this uranium nucleus in the entire process is the four protons that we discussed earlier plus the four neutrons in the 𝛼 particles. And so altogether, we lose eight nucleons.

And another way to work this out is that the uranium is producing at the end two 𝛼 particles. Now, each 𝛼 particle has four nucleons. So two 𝛼 particles will have eight nucleons. That’s two times four. And hence, the net effect is that the uranium nucleus is losing eight nucleons by the end of this process. So our answer is that there are eight nucleons in total ejected from a uranium nucleus that undergoes this process.

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