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

Hint: Wave number is the measure of number of wavelengths per unit length. It is also called spatial frequency. The wave number is represented as ‘k’. The wave number can also be defined as the number of complete cycles of waves present in a wavelength. The wave number is the quantity to measure the magnitude.

Complete step by step answer:
• The dimensional formula can be found by the formula of the certain quantities. The formula for the wave number, \[k = {1}{\lambda }\]
• The wavelength is the measure of length. Hence the dimensional formula for wavelength is \[{M^0}{L^1}{T^0}\]. As the wavelength is the inverse of the wave number, the dimensional formula for wave number is \[{M^0}{L^{ - 1}}{T^0}\]

Hence, the correct answer is option (B).

Additional information:
• The highest positive point in a wave is called ‘crest’ and the highest negative point in a wave is called ‘trough’. The wavelength is the distance between the crest and trough. The total number waves in a certain time period is called frequency. The reciprocal of time is called frequency.
• The wavelength and the frequency of the wave determine the type of electromagnetic radiation.
• The electromagnetic waves can be divided into different regions based on the wavelength and frequency. Electromagnetic waves have a velocity of $3 \times {10^8}m{s^{ - 1}}$ in vacuum.

Note: The wave number is the reciprocal of wavelength. It is the measure of the total number of complete cycles of waves present in the length of the wave. As it describes the number of waves present in the wavelength, wave number is the inversely proportional to the wavelength. Wave number is the scalar quantity.