Sample Exercise: Using the Rydberg Formula
What is the wavelength of the photon in the infrared series of the hydrogen spectrum for m = 6 and n = 3? Use the Rydberg formula.

Question

[latex]R = 1.097 × 10^{7} m^{-1}[/latex]

m = 6

n = 3

λ = ?

Accepted Answer

[latex]\frac{1}{λ}= R (\frac{1}{n^{2}}-\frac{1}{m^{2}})[/latex]

[latex]= 1.097 × 10^{7} m^{-1}(\frac{1}{3^{2}}-\frac{1}{6^{2}})[/latex]

[latex]= 1.097 × 10^{7} m^{-1}(\frac{1}{9}-\frac{1}{36})[/latex]

[latex]= 1.097 × 10^{7} m^{-1}(0.0833)[/latex]

[latex]\frac{1}{λ}= 9.14 × 10^{5} m^{-1}[/latex]

[latex]λ= \frac{1}{9.14 × 10^{5} m^{-1}}= 10.94 × 10^{-7} m[/latex]

Notice that this result is in the infrared region of the electromagnetic spectrum because its wavelength is greater than [latex]7.5 × 10^{–7}[/latex] m, as discussed on page 334 in Chapter 16. Notice also that the m appearing in the Rydberg formula is an integer and has nothing to do with the unit m–1, which is an inverse meter.

Question 18.2: Sample Exercise: Using the Rydberg Formula What is the wavel...

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