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

Options

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

Answer

To determine the element with the maximum binding energy per nucleon, we can follow these steps:

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

**Hint:** Recall that the binding energy per nucleon is an important indicator of nuclear stability.

### Step 2: Analyze the Binding Energy Curve
When we plot binding energy per nucleon against mass number (A), we observe a curve that initially rises, reaches a peak, and then begins to fall. This indicates that as mass number increases, the binding energy per nucleon increases up to a certain point.

**Hint:** Look for the trend in the graph of binding energy per nucleon versus mass number.

### Step 3: Identify the Maximum Point
From the graph, we find that the maximum binding energy per nucleon occurs at a mass number of approximately 56. This corresponds to the element iron (Fe), which has an atomic number of 26.

**Hint:** Remember that the peak of the curve is where the binding energy per nucleon is at its highest.

### Step 4: Confirm the Value
The maximum binding energy per nucleon for iron is about 8.8 MeV. This value is higher than that of other elements, such as helium, barium, and uranium.

**Hint:** Compare the binding energy values of other elements to confirm that iron has the highest value.

### Conclusion
Therefore, the binding energy per nucleon is maximum in the case of iron (Fe), which has a mass number of 56 and an atomic number of 26.

**Final Answer:** Iron (Fe), mass number 56.