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`

Explanation

To determine the value of the multiplication factor (k) for a nuclear reactor to be in a critical state, we can follow these steps:

### 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 next generation. Mathematically, it can be expressed as:
\[ k = \frac{N_{n}}{N_{n+1}} \]
where \(N_{n}\) is the number of neutrons in the current generation and \(N_{n+1}\) is the number of neutrons in the next 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 that cause fission in the next generation. Therefore, for a critical reactor:
\[ k = 1 \]

3. **Behavior of k**:
- If \(k < 1\):
- The reactor is subcritical, meaning that the number of neutrons decreases with each generation, leading to a failure to sustain the reaction.
- If \(k > 1\):
- The reactor is supercritical, which means the number of neutrons increases with each generation, potentially leading to an uncontrollable reaction or explosion.

4. **Conclusion**:
- For the operation of a nuclear reactor to be critical, the multiplication factor (k) must be equal to 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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