The dimensional formula of wave number is

Options

A. `M^(0)L^(0)T^(-1)`
B. `M^(-1)L^(-1)T^(0)`
C. `M^(0)L^(-1)T^(0)`
D. `M^(0)L^(0)T^(0)`

Answer

To find the dimensional formula of wave number, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Wave Number**:
- Wave number (denoted as \( \nu \) or \( \nu_{\text{bar}} \)) is defined as the number of wavelengths per unit distance. It is mathematically expressed as:
\[ \nu = \frac{1}{\lambda} \]
where \( \lambda \) is the wavelength.

2. **Identifying the Dimension of Wavelength**:
- Wavelength (\( \lambda \)) is a measure of distance. Therefore, its dimensional formula is:
\[ [\lambda] = L^1 \]
This can also be expressed in terms of base dimensions as \( M^0 L^1 T^0 \).

3. **Finding the Dimension of Wave Number**:
- Since wave number is the reciprocal of wavelength, we can express its dimensional formula as:
\[ [\nu] = \frac{1}{[\lambda]} = \frac{1}{L^1} = L^{-1} \]
- In terms of base dimensions, this can be written as:
\[ [\nu] = M^0 L^{-1} T^0 \]

4. **Final Result**:
- Therefore, the dimensional formula of wave number is:
\[ [\nu] = M^0 L^{-1} T^0 \]

### Conclusion:
The dimensional formula of wave number is \( M^0 L^{-1} T^0 \).