# Calculate Binding Energy per Nucleon for 2H, 24Mg, 32S & 238U

• Agarb
In summary, binding energy per nucleon is the amount of energy required to break apart a nucleus into its individual nucleons. It is calculated by dividing the total binding energy of a nucleus by the number of nucleons in the nucleus. 2H, 24Mg, 32S, and 238U are specifically chosen for this calculation to illustrate the trend of binding energy per nucleon as the number of nucleons increases. The trend is that the binding energy per nucleon increases up to a certain point, reflecting the stability of larger nuclei. Calculating binding energy per nucleon is important in understanding the stability and properties of different nuclei, as well as in nuclear reactions and determining the abundance of elements in the universe.
Agarb

## Homework Statement

Calculate the binding energy per nucleon for each of the following nuclei. (Use the table of atomic masses as necessary.)

(a) 2H

(b) 24Mg

(c) 32S

(d) 238U

These are all in MeV by the way.

E=mc^2

## The Attempt at a Solution

I found for example c:

32-31.972071= .027929

.027929*(3E8^2)/32

What am I doing wrong?

If you add units (always do this!), you should see an issue.
Another problem: protons and neutrons don't weight 1u.

## What is binding energy per nucleon?

Binding energy per nucleon is the amount of energy required to break apart a nucleus into its individual nucleons (protons and neutrons). It is a measure of the stability of a nucleus and is typically expressed in units of MeV per nucleon.

## How is binding energy per nucleon calculated?

The binding energy per nucleon is calculated by taking the total binding energy of a nucleus and dividing it by the number of nucleons in the nucleus. The binding energy can be calculated using the famous equation E=mc2, where E is the energy, m is the mass defect (difference between the mass of the nucleus and the sum of the masses of its individual nucleons), and c is the speed of light.

## Why are 2H, 24Mg, 32S, and 238U specifically chosen for this calculation?

These elements were chosen because they have varying numbers of nucleons and can help illustrate the trend of binding energy per nucleon as the number of nucleons increases. 2H (deuterium) has 2 nucleons, 24Mg has 24 nucleons, 32S has 32 nucleons, and 238U has 238 nucleons.

## What is the trend of binding energy per nucleon as the number of nucleons increases?

The trend is that the binding energy per nucleon increases as the number of nucleons increases, up to a certain point. This is due to the fact that larger nuclei have a stronger nuclear force holding the nucleons together, resulting in a more stable nucleus with a higher binding energy per nucleon. However, for very large nuclei, the repulsive forces between protons start to dominate, leading to a decrease in binding energy per nucleon.

## Why is calculating binding energy per nucleon important in nuclear physics?

Calculating binding energy per nucleon allows us to understand the stability and properties of different nuclei. It is also important in nuclear reactions, such as fusion and fission, as the difference in binding energy between reactants and products determines the amount of energy released or required in the reaction. Additionally, binding energy per nucleon is a key factor in determining the stability and abundance of elements in the universe.

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