# Binding energy of a nitrogen nucleus

• cosmictide
In summary, a carbon-12 atom fuses with a hydrogen nucleus to form a nucleus of nitrogen, which releases 1.95 MeV of energy.
cosmictide

## Homework Statement

Hi guys, any help here would be greatly appreciated.

I'm told that a carbon-12 atom fuses with a hydrogen nucleus with the atomic mass of 1 to form a nucleus of nitrogen releasing 1.95 MeV as a result.

I'm asked to write an equation of the reaction and work out the binding energy of the nitrogen nucleus if the binding energy for the hydrogen is 0 MeV and the binding energy for the carbon-12 is -92.2MeV.

The equation I managed to get is 12C + 1H = 13N + 1.95 MeV. Is this correct? Also how do I work out the binding energy of the nitrogen nucleus? I thought it might be -94.15 MeV but that seems too simple. Any help would be hugely appreciated.

cosmictide said:

## Homework Statement

Hi guys, any help here would be greatly appreciated.

I'm told that a carbon-12 atom fuses with a hydrogen nucleus with the atomic mass of 1 to form a nucleus of nitrogen releasing 1.95 MeV as a result.

I'm asked to write an equation of the reaction and work out the binding energy of the nitrogen nucleus if the binding energy for the hydrogen is 0 MeV and the binding energy for the carbon-12 is -92.2MeV.

The equation I managed to get is 12C + 1H = 13N + 1.95 MeV. Is this correct? Also how do I work out the binding energy of the nitrogen nucleus? I thought it might be -94.15 MeV but that seems too simple. Any help would be hugely appreciated.

Not familiar with how such equations are written, but I would have expected to see more detail, like counts of nucleons. On the net I see formalisms like [atomic mass/atomic number]element symbol, e.g. [12/6]C.
For the energy, I would have guessed (by conservation) the simple and obvious relationship between the initial and final binding energy totals and the energy released that you appear to have used.

1 person
haruspex said:
Not familiar with how such equations are written, but I would have expected to see more detail, like counts of nucleons. On the net I see formalisms like [atomic mass/atomic number]element symbol, e.g. [12/6]C.
For the energy, I would have guessed (by conservation) the simple and obvious relationship between the initial and final binding energy totals and the energy released that you appear to have used.

Thanks for your reply. I think I'll take your advice and rewrite the formula with the atomic mass and number included.

## 1. What is binding energy?

Binding energy is the amount of energy required to hold a nucleus together. It is the difference between the mass of an atom's individual protons and neutrons and the mass of the nucleus as a whole. This energy is released when the nucleus is formed and is responsible for the stability of an atom.

## 2. How is binding energy calculated for a nitrogen nucleus?

The binding energy of a nitrogen nucleus is calculated using the Einstein's famous equation, E=mc², where E is the binding energy, m is the mass defect of the nucleus (difference between the mass of the nucleus and the sum of its individual particles), and c is the speed of light. The binding energy of a nitrogen nucleus is approximately 104 MeV (million electron volts).

## 3. What factors affect the binding energy of a nitrogen nucleus?

The binding energy of a nitrogen nucleus is primarily affected by the number of protons and neutrons in the nucleus. As the number of particles increases, the binding energy also increases. Other factors that can affect the binding energy include the distance between particles, the strong nuclear force, and the electromagnetic force.

## 4. Why is the binding energy of a nitrogen nucleus important?

The binding energy of a nitrogen nucleus is important for understanding the stability and properties of atoms and nuclei. It is also essential for nuclear reactions and energy production. The release of binding energy is responsible for the immense power of nuclear reactions such as fusion and fission.

## 5. How does the binding energy of a nitrogen nucleus compare to other elements?

The binding energy of a nitrogen nucleus is relatively high compared to other elements. It falls in the middle range of binding energies for stable nuclei, with elements like iron and nickel having higher binding energies and lighter elements having lower binding energies. This is due to the balance between the strong nuclear force, which holds the nucleus together, and the electromagnetic force, which repels positively charged protons.

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