Question

The nucleus having highest binding energy per nucleon is:

• A. \({}^{16}_{8}O\)
• B. \({}^{56}_{26}Fe\)
• C. \({}^{208}_{84}Pb\)
• D. \({}^{4}_{2}He\)

Hint:

The binding energy per nucleon increases as we approach iron on the periodic table, making iron the most stable nucleus. Both lighter and heavier nuclei have lower binding energies per nucleon.

Answer 1

The Correct Option is B

Step 1: {Understanding Binding Energy per Nucleon} 
The binding energy per nucleon (\( BE/A \)) is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is an important measure of nuclear stability. The higher the binding energy per nucleon, the more stable the nucleus is. The binding energy per nucleon is typically highest for elements in the mid-range of the periodic table, particularly for elements around iron (\( {}^{56}_{26}Fe \)). 
Step 2: {Comparing the Nuclei} 
- Lighter nuclei, such as \( {}^{4}_{2}He \) (Helium-4), have a relatively low binding energy per nucleon. This is because the nucleons in lighter nuclei are not as tightly bound as in heavier nuclei. 
- Heavy nuclei, such as \( {}^{208}_{84}Pb \) (Lead-208), also tend to have lower binding energy per nucleon compared to mid-range nuclei. This is due to the electrostatic repulsion between the positively charged protons, which weakens the nuclear force that binds the nucleus together. 
- \( {}^{56}_{26}Fe \) (Iron-56), which has the highest binding energy per nucleon (around 8.8 MeV), is considered the most stable nucleus. This high binding energy per nucleon explains why nuclear fusion (such as in stars) generally produces energy by fusing lighter elements up to iron, and why fission of heavy elements releases energy. Thus, the correct answer is \( {}^{56}_{26}Fe \). 
 

Answer 2

Step 1: Understanding Binding Energy per Nucleon
The binding energy per nucleon refers to the average energy that binds each nucleon (proton or neutron) within a nucleus. It is calculated as: \[ \text{Binding Energy per Nucleon} = \frac{\text{Total Binding Energy of Nucleus}}{\text{Number of Nucleons}} \] A higher value indicates a more stable nucleus, as more energy is required to break it apart.

Step 2: Why is Iron-56 Special?
Iron-56, denoted as: \[ ^{56}_{26}\text{Fe} \] has been experimentally observed to have the highest binding energy per nucleon among all known nuclei. This makes it:

• Extremely stable
• A final product in many nuclear reactions (fusion in stars and fission of heavier nuclei)

This is why stellar fusion stops at iron — fusing elements heavier than iron consumes more energy than it releases.

 

Step 3: Comparing the Options
Let’s analyze the given options based on their typical binding energy per nucleon:

\( ^{4}_{2}\text{He} \) (Helium-4): High, but not the highest

\( ^{16}_{8}\text{O} \) (Oxygen-16): Fairly high

\( ^{208}_{84}\text{Pb} \) (Lead-208): Lower than iron due to its large size

\( ^{56}_{26}\text{Fe} \) (Iron-56): Highest binding energy per nucleon

 

Step 4: Final Conclusion
\[ \boxed{^{56}_{26}\text{Fe} \text{ has the highest binding energy per nucleon}} \] Hence, the correct answer is:

Option 2: \( ^{56}_{26}\text{Fe} \)