The most important use of studying nuclear fission and fusion process was to harness nuclear energy for useful purpose of humanity. Nuclear reactor is the machine designed to harness nuclear energy to electricity. The basic principle involved is fission of uranium to krypton and barium by slow moving neutrons as in following `""_(0)n^(1)+""_(92)^(235)Uto""_(32)^(96)Kr+""_(56)^(141)Ba+3_(0)n^(1)+Q(200MeV)` reaction:
But the difficulty is that one neutron striking with `""_(92)^(235)U` produces three (2.6 on an average) neutrons which can cause further fission The neutron intensity available for further fission is controlled by measuring reproduction factor defined as the average number of neutrons from each fission the causes further fission. Maximum value of K 2.6. For optimum operation of nuclear reactor, the value of Kis mentioned in Column-1 for various stages in Columu-Il match the correct columns :
`{:("Column-I","Column-II"),((A)K=1,(p)"Uncontrolled chain reaction"),((B)Klt1,(q)"Critical"),((C)Kge1,(r)"Sub critical"),((D)K~~25,(s)"Super critical"):}`

Answer

To solve the problem, we need to match the values of the reproduction factor \( K \) from Column-I with their corresponding descriptions in Column-II based on the principles of nuclear fission. Let's analyze each option step by step.

### Step 1: Understand the reproduction factor \( K \)
The reproduction factor \( K \) is defined as the average number of neutrons from each fission event that causes further fission. The behavior of the nuclear chain reaction depends on the value of \( K \):
- If \( K < 1 \): The chain reaction is subcritical, meaning not enough neutrons are produced to sustain the reaction.
- If \( K = 1 \): The chain reaction is critical, meaning it is stable and can sustain itself.
- If \( K > 1 \): The chain reaction is supercritical, meaning it will escalate as more neutrons are produced.
- If \( K \) is approximately equal to 25: This indicates an uncontrolled chain reaction, where the reaction can escalate uncontrollably.

### Step 2: Match the values with their descriptions
Now, we will match the values of \( K \) with the corresponding descriptions:

1. **\( K = 1 \)**:
- This corresponds to a **critical** state where the chain reaction is sustained.
- Match: **(B) K = 1 → (q) "Critical"**

2. **\( K < 1 \)**:
- This indicates a **subcritical** state where the chain reaction cannot sustain itself.
- Match: **(C) K < 1 → (r) "Subcritical"**

3. **\( K \geq 1 \)**:
- This indicates a **supercritical** state where the chain reaction is increasing.
- Match: **(D) K ≥ 1 → (s) "Supercritical"**

4. **\( K \approx 25 \)**:
- This indicates an **uncontrolled chain reaction** where the reaction can escalate uncontrollably.
- Match: **(A) K ≈ 25 → (p) "Uncontrolled chain reaction"**

### Final Matches
Now we can summarize the correct matches:
- (A) K ≈ 25 → (p) "Uncontrolled chain reaction"
- (B) K = 1 → (q) "Critical"
- (C) K < 1 → (r) "Subcritical"
- (D) K ≥ 1 → (s) "Supercritical"