The dimensional representation of wave number is

Options

A. (a)`M^(0)L^(0)T^(-1)`
B. (b)`M^(0)L^(-1)T^(0)`
C. (c)`M^(0)L^(0)T^(0)`
D. (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. Mathematically, it can be expressed as:
\[ k = \frac{1}{\lambda} \]
where \( \lambda \) is the wavelength.

### Step 2: Identify the Dimensions of Wavelength
The wavelength \( \lambda \) is a measure of distance, so its dimensional formula is:
\[ [\lambda] = [L] = L^1 \]
This means that the dimension of wavelength is length.

### Step 3: Determine the Dimensions of Wave Number
Since wave number is the reciprocal of wavelength, we can express its dimensions as:
\[ [k] = \frac{1}{[\lambda]} = \frac{1}{L^1} = L^{-1} \]
This means the dimensional formula for wave number is:
\[ [k] = M^0 L^{-1} T^0 \]
Here, \( M^0 \) indicates that mass does not play a role, \( L^{-1} \) indicates inverse length, and \( T^0 \) indicates that time does not play a role.

### Step 4: Finalize the Dimensional Representation
Thus, the dimensional representation of wave number is:
\[ M^0 L^{-1} T^0 \]

### Step 5: Check the Options
Given the options, we can identify that the correct option corresponding to the dimensional representation of wave number is:
\[ \text{Option B: } M^0 L^{-1} T^0 \]

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

---