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Found in: Page 1302

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Figure 42-17 shows the curve for the binding energy per nucleon ${\mathbf{∆}}{{\mathbit{E}}}_{\mathbf{b}\mathbf{e}\mathbf{n}}$ versus mass number A. Three isotopes are indicated. Rank them according to the energy required to remove a nucleon from the isotope, greatest first.

The rank of the points according to the energy required to remove a nucleon from the isotope is 2 > 3 > 1 .

See the step by step solution

## Step 1: Given data

The figure 42-17 of binding energy versus mass number is given.

## Step 2: Understanding the concept of binding energy per nucleon

The binding energy (BE) of a nucleus is equal to the amount of energy released in forming the nucleus, or the energy required in removing a nucleon from the shell of an isotope. A graph of binding energy per nucleon (BEN) versus atomic number A implies that nuclei divided or combined release an enormous amount of energy.

## Step 3: Calculation of the rank of the points according to their binding energy

Comparing the given graph to the experimental found binding energy per nucleon graph, we can clearly see that the binding energy of 60 MeV matches for the point 2. Thus, these nuclei have most stable nucleus with great nuclear forces to overcome a nucleon from their isotope.

No, similarly comparing graph given with the original graph 42-7, the binding energy of 8MeV matches for the point 3, while binding energy of 5 MeV matches the point 1.

Thus, the stability of isotopes according to their binding energy is 2 > 3 > 1.

Hence, from the concept, the rank of the points according to their energy required to remove a nucleon is given by 2 > 3 > 1 .