Fission of nuclei is possible because the binding energy per nuclei in them

Options

A. increases with mass number at low mass numbers
B. decreases with mass number at low mass numbers
C. increases with mass number at high mass numbers
D. decreases with mass number at high mass numbers

Explanation

To understand why fission of nuclei is possible, we need to analyze the concept of binding energy per nucleon and how it varies with mass number. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding Binding Energy per Nucleon
The binding energy per nucleon is a measure of the stability of a nucleus. It is the energy required to remove a nucleon from the nucleus. A higher binding energy per nucleon indicates a more stable nucleus.

**Hint:** Remember that stability in nuclear physics is often associated with higher binding energy per nucleon.

### Step 2: Graph of Binding Energy per Nucleon vs. Mass Number
If we plot a graph of binding energy per nucleon against mass number, we observe that the graph rises to a peak and then falls. The peak occurs around mass number 56, which corresponds to iron (Fe).

**Hint:** Visualizing the graph can help you understand the relationship between mass number and binding energy.

### Step 3: Behavior of Smaller Nuclei (Mass Number < 56)
For nuclei with a mass number less than 56, the binding energy per nucleon increases as they combine to form heavier nuclei. This process is known as nuclear fusion, where smaller nuclei fuse to form a more stable nucleus with a higher binding energy per nucleon.

**Hint:** Fusion occurs for lighter elements, leading to greater stability.

### Step 4: Behavior of Heavier Nuclei (Mass Number > 56)
For nuclei with a mass number greater than 56, the binding energy per nucleon decreases as the mass number increases. In this case, heavy nuclei can become unstable and can split into smaller nuclei, a process known as nuclear fission. The resulting daughter nuclei have a higher binding energy per nucleon than the original heavy nucleus.

**Hint:** Fission is associated with heavy nuclei, where splitting leads to increased stability.

### Step 5: Analyzing the Options
Now, let's analyze the provided options:
1. **Incorrect**: Fission is not explained by an increase in binding energy for low mass numbers.
2. **Incorrect**: The statement about low mass numbers does not support fission; it supports fusion.
3. **Incorrect**: The statement about high mass numbers increasing binding energy is false.
4. **Correct**: For high mass numbers, the binding energy per nucleon decreases with increasing mass number, which supports the fission process.

**Hint:** Carefully evaluate each option against the principles of binding energy and stability.

### Conclusion
The fission of nuclei is possible because, for heavy nuclei (mass number > 56), the binding energy per nucleon decreases. This decrease in binding energy indicates that splitting the nucleus into smaller, more stable nuclei is energetically favorable.

**Final Answer:** The correct option is 4, which states that for high mass numbers, binding energy per nucleon decreases with mass number.

---