The operation of a nuclear reactor is said to be critical, if the multiplication factor (k) has a value

Options

A. 1
B. 1.5
C. 2.1
D. 2.5

Answer

To determine the condition for a nuclear reactor to be in a critical state, we need to understand the concept of the multiplication factor (k).

### Step-by-Step Solution:

1. **Understanding the Multiplication Factor (k)**:
The multiplication factor (k) is defined as the ratio of the number of neutrons in one generation to the number of neutrons in the preceding generation. Mathematically, it can be expressed as:
\[ k = \frac{N_{n+1}}{N_n} \]
where \(N_{n+1}\) is the number of neutrons in the current generation and \(N_n\) is the number of neutrons in the previous generation.

2. **Critical Condition**:
A nuclear reactor is said to be in a critical state when the chain reaction is self-sustaining. This occurs when the number of neutrons produced in one generation is equal to the number of neutrons from the previous generation.

3. **Setting the Condition for Criticality**:
For the reactor to be critical, the multiplication factor (k) must equal 1:
\[ k = 1 \]
This implies that the number of neutrons produced in one generation is exactly equal to the number of neutrons from the previous generation.

4. **Implications of k = 1**:
When \(k = 1\):
- The neutron population remains constant.
- The chain reaction neither increases nor decreases, indicating a stable and controlled reaction.

5. **Conclusion**:
Therefore, the operation of a nuclear reactor is said to be critical if the multiplication factor (k) has a value of 1.

### Final Answer:
The operation of a nuclear reactor is said to be critical if the multiplication factor (k) has a value of **1**.

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