Yellow light emitted from a lamp has a wavelength of 580 nm. Find the frequency and wavenumber of this light.

Given : 

Wavelength (λ) = 580 nm 

To find : 

Frequency (ν), Wave number \(\bar v\) 

Formulae :

\(v\) = \(\frac{c}{\lambda}\), \(\bar v\) = \(\frac{1}{\lambda}\) 

Calculation : 

Wavelength of yellow light (λ) = 580 nm = 580 × 10^-9 m [1 nm = 10^-9m]

We know that frequency (ν) is related to wavelength as :

ν = \(\frac{c}{\lambda}\) 

Where, c, velocity of light = 3.0 × 10^-8 m s^-1

∴ ν = \(\frac{3.0\times 10^8 ms^{-1}}{580\times 10^{-9}m}\) 

= 5.17 × 10¹⁴ s^-1

Again, 

Wave number,

\(\bar v\) = \(\frac{1}{\lambda}\)

= \(\frac{1}{580\times 10^{-9}m}\) 

= 1.72 x 10⁶ m^-1

Frequency = 5.17 × 10¹⁴s^-1 and wave number = 1.72 × 10⁶m^-1