Question

The sun's hot inner layers produce a fairly continuous spectrum of radiation, from infra-red to X-rays. When this radiation passes through the cooler outer layers, which are majorly composed of hydrogen ( $\sim 91.2\%$ of all atoms is hydrogen), some wavelengths get absorbed. Ignoring the other elements composing the outer layers and considering only hydrogen, can you guess the longest missing wavelength in the rainbows we see on Earth?

• A. 121.6 nm
• B. 656.3 nm
• C. 486.1 nm
• D. There are no missing wavelengths in the rainbow - it’s an absolutely continuous spectrum.

Answer 1

The correct option is B 656.3 nm

The principal gas in the sun's outer layers is hydrogen. Ignoring the other minor components, we know the wavelengths corresponding to the dark lines in the absorption spectrum of hydrogen should be missing in the rainbow. But there are many different spectral sets - the Lyman series, the Balmer series, Paschen, Brackett. Which one should we consider?

Remember that only the Balmer series contains lines in the visible part of the electromagnetic spectrum. So if the rainbow is indeed an absorption spectrum, it should have missing wavelengths corresponding to lines in the Balmer series! What is the longest wavelength in the Balmer series? In the Rydberg formula, it would correspond to $n_1=2and{n}_2=3$,
$\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})=(1.097\times {10}^7)\times (\frac{1}{2^2}-\frac{1}{3^2})m^{-1}\Rightarrow \lambda =6.563\times {10}^{-7}m=656.3nm$