Identify the incorrectly matched set from the following
`{:("List - I","List - II"),("1) Wavelength","Nanometers"),("2) Frequency","Hertz"),("3) Wavenumber",m^(-1)),("4) Velocity","ergs"):}`

Answer

To identify the incorrectly matched set from the given options, we will analyze each item in List - I and compare it with its corresponding item in List - II.

### Step-by-Step Solution:

1. **Wavelength (List - I)**:
- Definition: Wavelength is the distance between two successive crests or troughs of a wave.
- Unit: The unit of wavelength is typically measured in nanometers (nm).
- **Match**: Wavelength - Nanometers (Correct)

2. **Frequency (List - I)**:
- Definition: Frequency is the number of occurrences of a repeating event per unit time.
- Unit: The unit of frequency is Hertz (Hz), which is equivalent to one cycle per second.
- **Match**: Frequency - Hertz (Correct)

3. **Wavenumber (List - I)**:
- Definition: Wavenumber is the number of waves per unit distance, defined as the reciprocal of wavelength (1/λ).
- Unit: The unit of wavenumber is typically expressed in meters inverse (m⁻¹).
- **Match**: Wavenumber - m⁻¹ (Correct)

4. **Velocity (List - I)**:
- Definition: Velocity is the distance traveled per unit time.
- Unit: The standard unit of velocity is meters per second (m/s).
- **Match**: Velocity - ergs (Incorrect)

### Conclusion:
The incorrectly matched set is:
- **Velocity - ergs** (This is incorrect because ergs is a unit of energy, not velocity).

### Final Answer:
The incorrectly matched set is **Velocity - ergs**.

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