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Using Rydberg's formula to find the first four wavelengths of the Lyman series.

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We compute the Lyman series using Rydberg's formula for the wavelengths: first four wavelengths in the Lyman series.

In this problem, we compute the first four wavelengths in the Lyman series by using Rydberg's empirical formula for the wavelengths emitted by hydrogen. The Lyman series is defined by transitions to the n=1 level of hydrogen. Note that Rydberg developed his formula empirically: there was no theory of electron energy level transitions here, just a mathematical pattern in the data! So, we look at the transition from n=2 to n=1, n=3 to n=1, n=4 to n=1, and so on, and we don't necessarily have to indicate that these are energy transitions in the hydrogen atom: we just use transitions to n=1 as the Lyman series (by the time the Bohr atom is developed, we think of these as transitions to the ground state of hydrogen).

So, we plug in the numbers for n_f and n_i and compute the wavelength in nanometers for each photon emitted from the hydrogen atom. We find that the Lyman series photons are ultraviolet, so these do not contribute to the color of excited hydrogen gas.