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Chapter 18: Q5P (page 456)

Characteristic orange light produced by sodium in a flame is due to an intense emission called the sodium D line, which actually a doublet, with wavelength (measured in vacuum) of 589.157 88 and 589.755 37 nm. The index of refraction of air at a wavelength near 589 nm is 1.000 292 6. Calculate the frequency, wavelength, and wavenumber of each component of the D line, measured in air.

Short Answer

Expert verified

Given data,

The frequency in vacuum isv=5.0869.1014Hz

The wavelength of air λair=589.58285nm

The wavenumber isv~=1.6961145.104cm-1

Step by step solution

01

Calculate frequency:

v=cλvaccum=3.108m/s2589.15788.10-9mv=5.0920.1014Hzv=cλvaccum=3.108m/s2589.75537.10-9mv=5.0869.1014Hz

02

Calculate wavelength of air:

λair=589.15788nm1.0002926λair=588.98554nmλair=589.75537nm1.0002926λair=589.58285nm

03

Calculate wavenumber:

v~=1λair=1588.98554nmv~=1.6978345.10-3nm-1v~=1.6978345.104cm-1v~=1λair=1589.58285nmv~=1.6961145.10-3nm-1v~=1.6961145.104cm-1

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