Chapter 24.3, Problem 27SSC

Interpretation Introduction

(a)

Interpretation:

The reason for the isotope ${}_{26}^{56}\text{Fe}$ to be highest on the curve needs to be explained.

Concept introduction:

The binding energy is defined as the energy required for breaking 1 mol of any nuclei into its individual nucleons.

Explanation of Solution

The graph is represented as follows:

The above graph shows a change in binding energy per nucleon with an increase in mass numbers.

This can be seen from the graph that isotope ${}_{26}^{56}\text{Fe}$ has the highest binding energy per nucleon that is it has the highest point on the curve.

The binding energy is defined as the energy required breaking 1 mol of any nuclei into its individual nucleons. If the binding energy per nucleon is large, the force by which the nucleons are held together will be strong and the nucleus will be more stable. The binding energy per nucleon is lower for less stable atoms.

Here, the element with a mass number near 60 is most stable and it has maximum binding energy per nucleon.

Interpretation Introduction

(b)

Interpretation:

Whether more stable isotopes are located higher or lower on the curve needs to be determined.

Concept introduction:

The binding energy is defined as the energy required breaking 1 mol of any nuclei into its individual nucleons. If the binding energy per nucleon is large, the force by which the nucleons are held together will be strong and nucleus will be more stable. The binding energy per nucleon is lower for less stable atoms.

Explanation of Solution

The more stable isotopes have large binding energy per nucleons. The energy increases on moving from bottom to top in the graph thus, the isotopes located higher on the curve have maximum binding energy per nucleons thus, they are more stable isotopes.

Interpretation Introduction

(c)

Interpretation:

The stability of Li-6 and He-4 needs to be compared.

Concept introduction:

The binding energy is defined as the energy required breaking 1 mol of any nuclei into its individual nucleons. If the binding energy per nucleon is large, the force by which the nucleons are held together will be strong and nucleus will be more stable. The binding energy per nucleon is lower for less stable atoms.

Explanation of Solution

The binding energy curve is represented as follows:

The points are represented for Li-6 and He-4. Here, mass number of Li is more than He but both are less than 60.

The binding energy per nucleon is less for Li-6 and it is approximately $5.2\times {10}^8\text{ kJ/mol}$ and that for He-4 is approximately $7.0\times {10}^8\text{ kJ/mol}$. The atom with more binding energy per nucleon is more stable thus; He-4 is more stable as compared to Li-6. The difference in binding energy is: $7\times {10}^8-5.2\times {10}^8=1.8\times {10}^8$.