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Chemistry Question on Developments Leading to the Bohr’s Model of Atom

Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber (v) of the yellow light

Answer

From the expression, λ=cvλ = \frac {c}{v}
We get,
v=cλv = \frac {c}{λ} ......(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):
v=3×108580×10−9v = \frac {3×10^8}{580×10^{-9}}
v=5.17×10−14s−1v = 5.17×10^{-14} s^{-1}
Thus, frequency of yellow light emitted from the sodium lamp
= 5.17×1014s−15.17×10^{14} s^{-1}
Wave number of yellow light,
vˉ=1λ\bar v= \frac 1λ
vˉ=1580×10−9\bar v= \frac {1}{580×10^{-9}}
vˉ=1.72×106 m−1\bar v= 1.72×10^6\ m^{-1}