A specific energetic beam of monochromatic light operates with a constant frequency of $6.0 imes 1

Question

A specific energetic beam of monochromatic light operates with a constant frequency of $6.0 	imes 10^{14} \mathrm{~Hz}$. The corresponding wave number ($\bar{
u}$) of this electromagnetic radiation travelling in a vacuum is

Professor PC Thomas Classes · Answer

(a) : The wave number is mathematically defined as the reciprocal of the wavelength: $\bar{
u} = \frac{1}{\lambda}$. Employing the wave equation $c = 
u \lambda$, we can substitute to get $\bar{
u} = \frac{
u}{c}$. Plugging in the values yields: $\bar{
u} = \frac{6.0 	imes 10^{14} \mathrm{~s}^{-1}}{3.0 	imes 10^8 \mathrm{~m/s}} = 2.0 	imes 10^6 \mathrm{~m}^{-1}$. Converting this result into $\mathrm{cm}^{-1}$ gives $2.0 	imes 10^6 \mathrm{~m}^{-1} 	imes \left(\frac{1 \mathrm{~m}}{100 \mathrm{~cm}}ight) = 2.0 	imes 10^4 \mathrm{~cm}^{-1}$. Hence, both numerical representations are valid.