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 \( {}^{56}_{26}Fe \).