Question

The dimensional formula of wave number is

• A. $M^0{L}^0{T}^0$
• B. $M^0{L}^{-1}{T}^0$
• C. $M^0{L}^0{T}^{-1}$
• D. $M^{-1}{L}^{-1}{T}^0$

Answer 1

The correct option is B

$M^0{L}^{-1}{T}^0$

Wave number: It is the reciprocal of wavelength, basically it represents the number of wavelengths fit in a unit length.

Step 1: Formula:

$\tilde{v}=\frac{1}{\lambda }$, Where $\lambda$ is the wavelength of the wave.

The dimensions of $\lambda$ is $M^0{L}^1{T}^0$

Step 2: Find the dimension of the wave number, $\tilde{v}$

⇒ The dimensional formula of $\tilde{v}$ is $\frac{1}{M^0{L}^1{T}^0}$

⇒ The dimensional formula of $\tilde{v}$ is $M^0{L}^{-1}{T}^0$

Hence, option B is the correct answer.