# Mass-Energy Conversion, Mass Defect and Nuclear Binding Energy

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• 1:07 Mass and Energy
• 2:05 Nuclear Binding Energy
• 2:47 Mass Defect
• 6:25 Lesson Summary

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Lesson Transcript
Instructor: Kristin Born

Kristin has an M.S. in Chemistry and has taught many at many levels, including introductory and AP Chemistry.

When you hear the term 'nuclear power,' what comes to mind? Do you know where that energy and power is coming from? In this lesson, we are going to zoom in on the nucleus of a helium atom to explain how something as small as a nucleus can produce an extremely large amount of energy.

## Introduction

You are going to the gas station and, for some reason, decide to put 3 kg of gasoline in your car. This is the equivalent of almost 1 gallon of gas (so, not much). It may get you somewhere around 25-35 miles, depending on the gas mileage of your vehicle, of course. 35 miles per gallon might seem great, and this is what you would get out of it if you combusted it in your car. Now, what if I told you that those 3 kg of fuel could take you around the Earth hundreds of times? If your car were equipped to run on nuclear energy instead of chemical energy (the combustion of gasoline), you would be able to get billions of times more energy out of the 3 kilograms of gasoline. At this point, having a nuclear powered car seems about as technologically far off as having a time machine. But the idea is that nuclear reactions produce much more energy than chemical reactions. Why?

## Mass and Energy

The energy involved in a nuclear reaction can be calculated using the well-known equation: E = mc2. In this equation, E stands for energy, m represents mass, and c stands for the speed of light, which is 3.0 x 108 m/s. If the mass is measured in kilograms (as in my opening example), then the amount of energy obtained from that amount of mass would be represented in joules, a common unit of energy in chemistry. What this equation states is that mass and energy are directly proportional to each other. If a substance gains mass, it will gain energy; if it loses mass, it will lose energy. This mass-energy conversion is really interesting because it usually deals with very small amounts of mass (barely even noticeable) and very high amounts of energy (enough to power a city).

## Nuclear Binding Energy

We are going to go into more detail on this by zooming in on just one alpha particle, or a helium nucleus. In nuclear symbols, we would write it like this. Now, let's imagine that the helium nucleus is busted up into little pieces. If this happened, it would require a great deal of energy, and just like there's a special name for the energy required to remove an electron (ionization energy), this great deal of energy required to separate the nucleus into its individual pieces has a special name: nuclear binding energy. The higher the nuclear binding energy, the more stable the nucleus, meaning that the really stable nuclei will require more energy to split up.

## Mass Defect

So far, we have discussed what happens when this little helium nucleus gets hit with a lot of energy - enough to break it up into its smaller pieces. So, let's write this in equation form. So, here is our helium nucleus, represented by 4, 2, He - 4 being the mass number, or the number of particles in the nucleus (protons and neutrons), and 2 being the atomic number, or the number of protons. We are then going to use a plus sign and write out the word 'energy' because we are adding energy to this little guy. We're going to go a little further and write down the mass of our helium nucleus. If we report out a very accurate mass of a helium nucleus, many places past the decimal, we get a mass of 4.00150 amu.

Next, we are going to draw our arrow, indicating that a change will take place once all of this energy is added, and on the other side, we write out each particle that is created: 2 protons (each symbolized as 1, 1, p) and 2 neutrons (each symbolized as 1, 0, n). Finally, we will write down the mass of each of these particles measured out many places past the decimal. Usually, we express the mass of a proton as 1 amu, which is acceptable in most situations. In this situation, however, we need to be more precise. The mass of a proton measured out to 6 significant figures is 1.00728 amu. The same applies for the mass of a neutron. Usually, it is reported as 1 amu but measured out to 6 significant figures, we have 1.00866 amu.

Do you notice anything strange about these masses? What if we add up the masses of each of the four particles? We get a total mass of 4.03188 amu. That is 0.03038 amu higher than the mass we started out with! This difference in mass is called mass defect. Mass defect is basically the difference between the mass of a nucleus and its pieces. And by 'pieces,' I mean specifically its nucleons, or its protons and neutrons.

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