Yellow light emitted from a lamp has a wavelength of 580 nm. Find the

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

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

Answer»

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