When the number of nucleons in a nuclues increases the binding energy per nucleon

Options

A. increases continuously with mass number
B. decreases continuously with mass number
C. remians constant with mass number
D. first increases and then decreases with increases of mass number

Answer

To solve the question regarding the relationship between the number of nucleons in a nucleus and the binding energy per nucleon, we can follow these steps:

### Step 1: Understand the Concept of Binding Energy
Binding energy is the energy required to disassemble a nucleus into its individual nucleons (protons and neutrons). The binding energy per nucleon is the binding energy divided by the total number of nucleons in the nucleus.

**Hint:** Recall that binding energy is a measure of the stability of a nucleus.

### Step 2: Define Nucleons
Nucleons refer to the particles found in the nucleus, which include protons and neutrons. The total number of nucleons in a nucleus is known as the mass number (A).

**Hint:** Remember that mass number (A) = Number of protons (Z) + Number of neutrons (N).

### Step 3: Analyze the Binding Energy Curve
The binding energy per nucleon versus mass number curve shows how the binding energy changes as the number of nucleons increases. Initially, as the mass number increases, the binding energy per nucleon increases.

**Hint:** Look for patterns in the binding energy curve, especially around the region of iron (Fe).

### Step 4: Identify the Maximum Point
For elements around iron (specifically iron-56), the binding energy per nucleon reaches a maximum value of approximately 8.8 MeV. Beyond this point, as the mass number continues to increase, the binding energy per nucleon starts to decrease.

**Hint:** Consider why iron is often referred to as the most stable nucleus.

### Step 5: Conclude the Relationship
From the analysis, we conclude that as the number of nucleons in a nucleus increases, the binding energy per nucleon first increases, reaches a maximum, and then decreases. Therefore, the statement "when the number of nucleons in a nucleus increases, the binding energy per nucleon first increases and then decreases" is correct.

**Hint:** Summarize the behavior of binding energy per nucleon in relation to mass number.

### Final Answer
The binding energy per nucleon first increases with an increase in the number of nucleons, reaches a maximum around iron-56, and then decreases as the mass number continues to increase.