Question

Yellow light emitted from a sodium lamp has a wavelength (\[\lambda \]) of 580nm. Calculate the frequency (v) and wavelength (\[\overline \nu\]) of the yellow light.

Answer 1

Hint: Wavelength is the distance between identical points in the adjacent cycles of a waveform signal propagated in space or along a wire. Wavelength is inversely proportional to the frequency.

Complete step by step answer:
Given: Wavelength of yellow light is 580nm. Wavelength is shown by \[\lambda \].
\[\lambda \] is equal to the speed (v) of a wave train in a medium divided by its frequency (f)
\[\lambda \]= \[\dfrac{v}{f}\]
And as we know, 1 nanometer = \[1 \times {10^{ - 9}}\] meter, so wavelength is \[580 \times {10^{ - 9}}\]m
And frequency (v) = \[\dfrac{c}{\lambda } = \dfrac{{3 \times {{10}^8}}}{{580 \times {{10}^{ - 9}}}}\]= \[5.17 \times {10^{14}}/s\]
Where, c is defined as the speed of light and it is a constant value and its value is equal to the \[3 \times {10^8}\]m/s. This speed is in vacuum itself.
Now, we have to calculate the wave number.
Wave number is defined as the number of wavelengths which can be accommodated in 1 cm length along the direction of propagation. It is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distances. Whereas temporal frequency can be thought of as the number of waves per unit distance.
Wave number of yellow light is given by:
\[\overline \nu = \dfrac{1}{\lambda }\]
We have \[\lambda \]= 580 nm (given) use this value in given equation:
\[\overline \nu \] = \[\dfrac{1}{{580 \times {{10}^{ - 9}}}}\]
\[\overline \nu \] = \[1.72 \times {10^6}{m^{ - 1}}\]

Note: Don’t get confused with the term wavenumber and wavelength both are different and the main difference in between them is wavelength is the distance between two consecutive points of wave of the wave and wave number is defined as the number of wavelengths in a given distance.