In Bohr's atomic model for hydrogen like atoms match the following column :
`{:(,"Column I",,"Column II"),((A),"If electron jumps from n = 32 to n = 1",(p),"Speed of electron will become 2 times"),((B),"If electron jumps from n = 1 to n = 4",(q),"Kinetic energy of electron will become 4 time"),((C),"If electron jumps from n = 4 to n = 4",(r),"Angular momentum of electron will becomes 2 times"),(,,(s),"Angular velocity of electron will becomes 4 times"),(,,(t),"None"):}`.

Explanation

To solve the problem of matching the columns based on Bohr's atomic model for hydrogen-like atoms, we will analyze the relationships between the quantum number \( n \) and the properties of the electron: speed, kinetic energy, angular momentum, and angular velocity.

### Step-by-Step Solution:

1. **Understanding the Relationships**:
- **Speed of Electron (V)**: The speed of the electron is inversely proportional to the principal quantum number \( n \):
\[ V \propto \frac{1}{n} \]
- **Kinetic Energy (KE)**: The kinetic energy of the electron is inversely proportional to the square of the principal quantum number \( n \):
\[ KE \propto \frac{1}{n^2} \]
- **Angular Momentum (L)**: The angular momentum of the electron is directly proportional to the principal quantum number \( n \):
\[ L \propto n \]
- **Angular Velocity (ω)**: Angular velocity can be expressed as:
\[ \omega = \frac{V}{r} \]
where \( r \) is the radius of the orbit, which is proportional to \( n^2 \). Thus, we find:
\[ \omega \propto \frac{1}{n^3} \]

2. **Analyzing Each Case**:
- **Case A**: Electron jumps from \( n = 32 \) to \( n = 1 \):
- Speed: \( V \) increases by a factor of \( 32 \) (since \( V \propto \frac{1}{n} \)).
- Kinetic Energy: \( KE \) increases by a factor of \( 32^2 = 1024 \).
- Angular Momentum: \( L \) increases by a factor of \( 32 \).
- Angular Velocity: \( \omega \) increases by a factor of \( 32^3 = 32768 \).
- **Match**: None of the options in Column II match.

- **Case B**: Electron jumps from \( n = 1 \) to \( n = 4 \):
- Speed: \( V \) decreases by a factor of \( 4 \).
- Kinetic Energy: \( KE \) decreases by a factor of \( 4^2 = 16 \).
- Angular Momentum: \( L \) increases by a factor of \( 4 \).
- Angular Velocity: \( \omega \) decreases by a factor of \( 4^3 = 64 \).
- **Match**: None of the options in Column II match.

- **Case C**: Electron jumps from \( n = 4 \) to \( n = 4 \):
- No change in any property.
- **Match**: None of the options in Column II match.

3. **Final Matching**:
- **A**: None (t)
- **B**: None (t)
- **C**: None (t)

### Final Answer:
- A - t (None)
- B - t (None)
- C - t (None)