Why does a given nucleus have less mass than the sum of its constituent protons and neutrons?

Video transcript

Welcome back everyone explain why the actual mass of the nucleus is not exactly equal to the sum of the masses of its constituent neutrons and protons. Looking at statement A. It says that the actual mass of the nucleus is not exactly equal to the sum of the masses of its constituent neutrons and protons because some mass is lost in the universe. So let's imagine our nucleus of any atom. We want to recall that what makes up our nucleus are our protons and neutrons which are bound together and held together by the strong nuclear force. Recall that as a unit are protons and neutrons are considered nucleons which make up our nucleus. Next we want to recall our concept of binding energy delta E. Recall that are binding energy is going to be the energy that is required to separate our nucleons. Now, our binding energy can also be interpreted as our energy that is used to hold our protons and neutrons together in the nucleus, meaning that the mass of our nucleons gets converted to energy, which is why we have our mass energy equivalence formula outlined by scientists like Einstein. So when the prompt states for choice A. That mass is lost in the universe, they're not specific enough. Mass is not lost but it's rather converted into energy. And so ultimately that means that mass is conserved, mass and energy are conserved. So we would actually say that statement A is false because we would correct it to say that mass is conserved. So we would rule out choice A. And now let's consider statement B, the difference in mass is converted to energy. We can agree with that and occurs either when protons and neutrons bind to form the nucleus or when a nucleus is broken apart into its constituent particles. And that is exactly what we just defined for our binding energy. The lost mass of our nucleons gets converted into energy. And so when our mass decreases, this will correspond to an increase in energy. And it also works the other way around. When mass increases, our energy will decrease. So we can also recognize that the some of our masses of our protons and neutrons within our nucleus would be equivalent to our mass of our nucleus plus our mass defect. And we can also say that the sum of our mass of protons to neutrons is also equal to our mass of our nucleus plus our binding energy represented by delta E. Since we understand that mass and energy are conserved. And so overall we would agree that statement B is definitely a true statement. So right now it's looking like a correct choice. Let's put a checkmark there. Moving onto statement, see the difference in masses is only due to a rounding off air because the mass of the nucleus should always be equal to the sum of masses of its constituent particles we outlined based on what we observed in choice B. That it's not due to a rounding off air. The difference in mass is is due to as we stated, our mass defect getting converted to binding energy. And we also outlined below that the mass of the constituent particles being are protons and neutrons in our nucleus is not just equal to the mass of our nucleus, but it's equal to the mass of our nucleus plus our mass defect and plus are binding energy. And so we can agree that statement C is a false statement. So we'll rule it out from our options. Next we have choice D, which reads that this only applies to hydrogen one and is due to the fact that it is too small. We can agree that statement D. Is not true. It it's false because it does not explain why our mass of our nucleus is not exactly equal to the sum of the masses of its protons and neutrons. Because we outlined below that our mass is conserved as energy here. And so what we would observe with mass defect in the nucleus is going to be true for all reactions. And so that means that statement is false. We can rule it out. And the only correct answer to complete this example is going to be statement be the difference in mass is converted to energy and occurs either when protons and neutrons bind to form the nucleus or when a nucleus has broken apart into its constituent particles. And this will properly explain why the actual mass of the nucleus is not equal to the sum of the masses of its constituent neutrons and protons. So B is the final answer. I hope that this made sense and let us know if you have any questions.