The graph between the binding energy per nucleon (E) and atomic mass number (A) is as-

Options

A.
B.
C.
D.

Answer

To solve the question regarding the graph between binding energy per nucleon (E) and atomic mass number (A), we will follow these steps:

### Step 1: Understand the Definitions
- **Binding Energy (BE)**: This is the energy required to disassemble a nucleus into its constituent protons and neutrons.
- **Binding Energy per Nucleon (E)**: This is the binding energy divided by the total number of nucleons (protons + neutrons). It gives an idea of how tightly bound the nucleons are within the nucleus.

### Step 2: Relate Binding Energy to Atomic Mass Number
- The atomic mass number (A) is defined as the total number of nucleons in a nucleus, i.e., A = Z + N, where Z is the number of protons and N is the number of neutrons.

### Step 3: Analyze the Trend of Binding Energy per Nucleon
- As the atomic mass number (A) increases, the binding energy per nucleon initially increases. This is due to the strong nuclear force that acts between nucleons, which becomes more effective as more nucleons are added to the nucleus.
- After reaching a certain point, the binding energy per nucleon starts to decrease. This is because, as the nucleus gets larger, the repulsive forces between protons (which are positively charged) begin to outweigh the attractive forces, leading to a decrease in binding energy per nucleon.

### Step 4: Sketch the Graph
- The graph will show binding energy per nucleon (E) on the y-axis and atomic mass number (A) on the x-axis.
- Initially, the graph will rise, indicating an increase in binding energy per nucleon with increasing A.
- After reaching a peak, the graph will start to decline, indicating a decrease in binding energy per nucleon as A continues to increase.

### Step 5: Identify the Correct Option
- Based on the analysis, the correct representation of the graph is one that shows an initial increase followed by a decrease in binding energy per nucleon as atomic mass number increases.

Thus, the answer is option number four, which correctly depicts this trend.

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