Nuclear Binding Energy: Videos & Practice Problems

Nuclear binding energy, denoted as E, is crucial in understanding the stability of isotopes and the conversion between mass and energy. This energy is released when an isotope forms, and conversely, it is absorbed when the isotope breaks apart. The formula:

$E=m{c}^2$

where E is the nuclear binding energy in joules, m is the mass defect in kilograms, and c is the speed of light (3.00 x 10⁸ m/s), quantifies this relationship. A higher nuclear binding energy indicates a more stable nucleus. This concept is pivotal in nuclear chemistry, as it allows for the calculation of either the nuclear binding energy or the mass defect when one of these quantities is known, thereby providing insight into the isotope's stability. Understanding this energy conversion is fundamental to grasping the principles of nuclear reactions and their applications.

Nuclear Binding Energy

Now, nuclear binding energy is involved in our discussion of mass to energy conversions back and forth. We're going to say if the mass defect is known, then its conversion to energy can be determined. We're going to say nuclear binding energy, which uses the variable E, is the energy that is released during the formation of an isotope. We're going to say recall. The process can also be seen as energy being absorbed to break up the isotope.

Now here we're going to say that the higher the nuclear binding energy, then the more stable the nucleus will be for any given isotope. With nuclear binding energy, we have our own formula here. We're going to say the formula for nuclear binding energy is per one mole of a radioisotope, and we're going to say nuclear binding energy, which is E=MC2. So our equation that we associate with Albert Einstein here, E is our nuclear binding energy, typically units of Joules.

From here, once you know joules, you can change to kilojoules or even megaelectron volts. Here we're going to say M is our mass defect in this instance. It's not going to be in atomic mass units. It needs to be in kilograms because of the presence of joules. That's because remember 1 Joule is equal to kilograms times meters squared over a second squared. Now the meter squared and the second squared come from squaring C, which is our speed of light.

Remember, speed of light is equal to 30×108 meters per second. All of these variables together help us to calculate nuclear binding energy. Remember, if you know nuclear binding energy, you can use it to determine your mass defect, and if you know your mass defect, you can use that to determine the nuclear binding energy. They're connected to each other through this formula.

Nuclear Binding Energy Example

Here it says calculate the nuclear binding energy in mega electron volts per mole of beryllium 10. Here we're told the atomic mass of beryllium 10 is 10.0135347 AMU. All right, so step zero is. We'll repeat steps one to three of the previous topic to calculate the mass defect of the radioisotope, so beryllium 10. So beryllium has an atomic number 4. It has four protons, 4 electrons and 10 -, 4 six neutrons.

Here we would find out what the complete total mass of all of these subatomic particles are to help us determine our predicted mass. So here we multiply them by their masses in AMU. So we multiply them across and we add the mall together. That's going to give us our predicted mass. So our predicted massage equals 10.08324 AMU. Here they're giving us the atomic mass. The atomic mass is related to our nuclear mass, which is 10.0135347 AMU. Subtracting these two gives us our mass defect, which is M. The mass defect here would be 0.0697053 AMU.

All right, So now that we have that, what we would do next is we would have to convert AMU into kilograms. And here we have a conversion that one AMU is equal to 1.66×10-27 kilograms. All right. So here we're going to say one AMU is 1.66×10-27 kilograms. So when we do that, we would get 1.1571×10-28 kilograms. This is important to remember because remember 1 Joule is equal to kilograms times meter squared over second squared. That's why we need to convert AMU into kilograms.

At this point we'd say that our nuclear binding energy is equal to mass defect times speed of light squared. So plug in what we just found for mass defect times our speed of light squared. When we do that, that's going to give me 1.041×10-11 kg times meter squared over second squared or Joules. Remember, when we're using this formula for calculating nuclear binding energy, it is equal to 1 mole of that radioisotope. So this is joules per one mole.

Now in this question, I don't want Jules per mole, they want Mega Electron Volts per mole. So we'd use the other conversion factor that we have here, where we have one Mega Electron Volt equal to 1.60×10-13 Joules. Here, Joules would cancel out and we'd be left with Mega Electron Volts per mole. Here this would come out to be 65.087 Mega Electron Volts per mole O. This would be our final answer.

Calcium-41 is commonly used radioisotope in the study of osteoporosis. If calcium-41 has a mass of 40.962278 amu, determine the nuclear binding energy per nucleon in MeV. (1 amu = 1.66 x 10^-27 kg). (1 MeV = 1.60 x 10^-13 J)

• A. 17.5537 MeV/nucleon
• B. 5.75533 MeV/nucleon
• C. 8.56276 MeV/nucleon
• D. 7.87683 MeV/nucleon

Answer: (C)

Calculate the mass defect (in g/mol) for the formation of a helium-6 nucleus, and calculate the binding energy in (MeV)/nucleon. (1 amu = 1.66 x 10^-27 kg). (1 neutron = 1.00866 amu 1 proton = 1.00727 amu, & 1 electron = 0.00055 amu) (1 MeV = 1.60 x 10^-13 J). 

• A. 0.04267 g/mol, 2.122 MeV/nucleon
• B. 0.05318 g/mol, 7.050 MeV/nucleon
• C. 0.05219 g/mol, 8.017 MeV/nucleon
• D. 0.05138 g/mol, 7.996 MeV/nucleon

Answer: (D)

Here’s what students ask on this topic:

What is nuclear binding energy?

Nuclear binding energy is the energy required to disassemble a nucleus into its component protons and neutrons. It's a measure of the stability of a nucleus; the greater the binding energy, the more stable the nucleus. This energy arises from the strong nuclear force, which is the force that holds the protons and neutrons together inside the nucleus, overcoming the repulsive electromagnetic force between the positively charged protons.

When nucleons (protons and neutrons) come together to form a nucleus, they release energy. This released energy is equivalent to the nuclear binding energy. It can be calculated using Einstein's famous equation,

$E=m{c}^2$

where 'E' is the energy, 'm' is the mass defect (the difference in mass between the bound nucleons and the nucleus), and 'c' is the speed of light. Nuclear reactions, such as fission (splitting of a nucleus) and fusion (combining of nuclei), involve changes in binding energy, which result in the release or absorption of large amounts of energy.

Which statement describes nuclear binding energy?

Nuclear binding energy is the energy required to disassemble a nucleus into its component protons and neutrons. It's a measure of the stability of a nucleus; the greater the binding energy, the more stable the nucleus. This energy comes from the strong nuclear force, which is the force that holds the nucleus together, overcoming the repulsive electromagnetic force between the positively charged protons.

When nucleons (protons and neutrons) are bound together in a nucleus, they have a lower total energy than when they are separate. This difference in energy is the nuclear binding energy, which can be calculated using Einstein's equation,

$E=m{c}^2$

where E is the energy, m is the mass defect (the difference between the mass of the bound nucleons and the total mass of the individual nucleons), and c is the speed of light. This binding energy is released in nuclear reactions, such as fission and fusion, which power nuclear reactors and stars, respectively.

Does nuclear energy represent a release of what binding force?

Nuclear energy is released from the strong nuclear force, also known as the strong interaction or strong force. This is one of the four fundamental forces in nature and is responsible for holding the protons and neutrons together within an atomic nucleus. When a nucleus undergoes a nuclear reaction, such as fission (splitting) or fusion (combining), the strong nuclear force is altered, and energy is released as a result.

In fission, a heavy nucleus splits into smaller nuclei, releasing energy, while in fusion, light nuclei combine to form a heavier nucleus, also releasing energy. The difference in binding energy before and after such reactions accounts for the energy produced, which is explained by Einstein's equation:

$E=m{c}^2$

where E is energy, m is mass, and c is the speed of light. This equation shows that even a small amount of mass can be converted into a large amount of energy, which is the principle behind nuclear power.