Q5P Characteristic orange light prod... [FREE SOLUTION]

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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 is $v = 5.0869 . 10^{14} Hz$

The wavelength of air $位_{air} = 589.58285 nm$

The wavenumber is $\tilde{v} = 1.6961145 . 10^{4} {cm}^{- 1}$

Step by step solution

Calculate frequency:

$v = \frac{c}{位_{va ccum}} = \frac{3 . 10^{8} m / s^{2}}{589.15788 . 10^{- 9} m} v = 5.0920 . 10^{14} Hz v = \frac{c}{位_{va ccum}} = \frac{3 . 10^{8} m / s^{2}}{589.75537 . 10^{- 9} m} v = 5.0869 . 10^{14} Hz$

Calculate wavelength of air:

$位_{air} = \frac{589.15788 nm}{1.0002926} 位_{air} = 588.98554 nm 位_{air} = \frac{589.75537 nm}{1.0002926} 位_{air} = 589.58285 nm$

Calculate wavenumber:

$\tilde{v} = \frac{1}{位_{air}} = \frac{1}{588.98554 nm} \tilde{v} = 1.6978345 . 10^{- 3} {nm}^{- 1} \tilde{v} = 1.6978345 . 10^{4} {cm}^{- 1} \tilde{v} = \frac{1}{位_{air}} = \frac{1}{589.58285 nm} \tilde{v} = 1.6961145 . 10^{- 3} {nm}^{- 1} \tilde{v} = 1.6961145 . 10^{4} {cm}^{- 1}$