Question.
Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wave number $(\bar{v})$ of the yellow light
Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wave number $(\bar{v})$ of the yellow light
Solution:
From the expression
$\lambda=\frac{\mathrm{c}}{v}$
We get
$v=\frac{c}{\lambda}$..........(i)
Where, ν= frequency of yellow light
$\mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
$\lambda=$ wavelength of yellow light $=580 \mathrm{~nm}=580 \times 10^{-9} \mathrm{~m}$
Substituting the values in expression (i):
$v=\frac{3 \times 10^{8}}{580 \times 10^{-9}}=5.17 \times 10^{14} \mathrm{~s}^{-1}$
Thus, frequency of yellow light emitted from the sodium lamp =
$5.17 \times 10^{14} \mathrm{~s}^{-1}$
Wave number of yellow light $\bar{v}=\frac{1}{\lambda}$,
$=\frac{1}{580 \times 10^{-9}}=1.72 \times 10^{6} \mathrm{~m}^{-1}$
From the expression
$\lambda=\frac{\mathrm{c}}{v}$
We get
$v=\frac{c}{\lambda}$..........(i)
Where, ν= frequency of yellow light
$\mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
$\lambda=$ wavelength of yellow light $=580 \mathrm{~nm}=580 \times 10^{-9} \mathrm{~m}$
Substituting the values in expression (i):
$v=\frac{3 \times 10^{8}}{580 \times 10^{-9}}=5.17 \times 10^{14} \mathrm{~s}^{-1}$
Thus, frequency of yellow light emitted from the sodium lamp =
$5.17 \times 10^{14} \mathrm{~s}^{-1}$
Wave number of yellow light $\bar{v}=\frac{1}{\lambda}$,
$=\frac{1}{580 \times 10^{-9}}=1.72 \times 10^{6} \mathrm{~m}^{-1}$