The dimensional representation of wave number is

Options

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

Answer

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

### Step 1: Understand the Definition of Wave Number
Wave number (denoted as \( k \)) is defined as the number of wavelengths per unit distance. It is mathematically expressed as:
\[ k = \frac{1}{\lambda} \]
where \( \lambda \) is the wavelength.

### Step 2: Identify the Dimension of Wavelength
The dimension of wavelength (\( \lambda \)) is a measure of length. Therefore, we can express the dimension of wavelength as:
\[ [\lambda] = L \]
where \( L \) represents the dimension of length.

### Step 3: Calculate the Dimension of Wave Number
Since wave number is the reciprocal of wavelength, we can write:
\[ [k] = \frac{1}{[\lambda]} = \frac{1}{L} \]
This can be expressed in terms of dimensions as:
\[ [k] = L^{-1} \]

### Step 4: Conclusion
Thus, the dimensional representation of wave number is:
\[ L^{-1} \]

### Final Answer
The dimensional representation of wave number is \( L^{-1} \).

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