The binding energy per nucleon is maximum in the case of.

Options

A. `._(2)He^(4)`
B. `._(26)Fe^(56)`
C. `._(56)Ba^(141)`
D. `._(92) U^(235)`

Answer

To determine which element has the maximum binding energy per nucleon among helium, iron, barium, and uranium, we can follow these steps:

### Step 1: Understand Binding Energy per Nucleon
The binding energy per nucleon is a measure of the stability of a nucleus. It is defined as the total binding energy of the nucleus divided by the number of nucleons (protons and neutrons). A higher binding energy per nucleon indicates a more stable nucleus.

### Step 2: Analyze the Elements
We need to consider the binding energy per nucleon for the given elements:
- **Helium (He)**: A light nucleus with relatively low binding energy per nucleon.
- **Iron (Fe)**: A medium-sized nucleus known to have one of the highest binding energies per nucleon.
- **Barium (Ba)**: A heavier nucleus, which typically has a lower binding energy per nucleon than iron.
- **Uranium (U)**: A very heavy nucleus, which also tends to have lower binding energy per nucleon.

### Step 3: Refer to the Binding Energy Curve
The graph of binding energy per nucleon versus mass number (A) shows that:
- Binding energy per nucleon increases with mass number up to a certain point (around iron, A ≈ 56).
- After iron, the binding energy per nucleon decreases for heavier nuclei.

### Step 4: Identify the Maximum
From the analysis and the binding energy curve:
- Iron (Fe) has the maximum binding energy per nucleon, approximately 8.8 MeV.

### Conclusion
Thus, the element with the maximum binding energy per nucleon among the given options is **iron (Fe)**.

### Final Answer
**Iron (Fe)** has the maximum binding energy per nucleon.

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