The average binding energy per nucleon is maximum for the nucleus

Options

A. `""_(2)He^(4)`
B. `""_(8)O^(16)`
C. `""_(26)Fe^(36)`
D. `""_(92)U^(238)`

Answer

To determine the nucleus for which the average binding energy per nucleon is maximum, we can follow these steps:

### Step 1: Understand Binding Energy per Nucleon
Binding energy per nucleon is defined as the total binding energy of a nucleus divided by the number of nucleons (protons and neutrons) in that nucleus. It indicates how tightly the nucleons are bound together in the nucleus.

### Step 2: Analyze the Binding Energy Curve
The binding energy per nucleon can be plotted against the atomic number (Z). This graph typically shows that as the atomic number increases, the binding energy per nucleon increases to a certain point and then starts to decrease.

### Step 3: Identify Key Elements
From the graph, we can identify key elements:
- The curve starts at hydrogen (H) with a low binding energy per nucleon.
- It rises and reaches a peak at iron (Fe), specifically at iron-56 (Fe-56).
- After reaching the peak, the binding energy per nucleon starts to decrease for heavier elements like uranium (U).

### Step 4: Determine the Maximum Point
The maximum point on the binding energy per nucleon graph occurs at iron-56. This indicates that iron-56 has the highest average binding energy per nucleon compared to other nuclei.

### Conclusion
Thus, the nucleus for which the average binding energy per nucleon is maximum is **iron-56 (Fe-56)**.