Question

Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wave number (${\displaystyle \overline{v}}$) of the yellow light.

Answer 1

From the expression,

${\displaystyle \lambda =\frac{\text{c}}{\text{v}}}$

We get,

${\displaystyle \text{v}=\frac{\text{c}}{\lambda }}$  ....(i)

Where,

ν = frequency of yellow light

c = velocity of light in vacuum = 3 × 10⁸ m/s

λ = wavelength of yellow light = 580 nm = 580 × 10^–9 m

Substituting the values in expression (i):

${\displaystyle \text{v}=\frac{3\times {10}^8}{580\times {10}^{-9}}=5.17\times {10}^{14}{\text{s}}^{-1}}$

Thus, frequency of yellow light emitted from the sodium lamp

= 5.17 × 10¹⁴ s^–1

Wave number of yellow light, ${\displaystyle \overline{v}=\frac{1}{\lambda }}$

${\displaystyle =\frac{1}{580\times {10}^{-9}}=1.72\times {10}^6 {\text{m}}^{-1}}$