What is the longest wavelength of electromagnetic radiation capable of ionizing a ground state hydrogen atom? report your answer in nanometers?

We can use Rydberg's formula to find the wavelength if we know the energy levels. The formula is: 1/w = R(1/L² - 1/U²) where w is the wavelength, L is the lower energy level, U the upper energy level, and R is Rydberg's constant, experimentally found to be 10,967,758 waves per meter for hydrogen. If the atom is in the n=6 state, that means the lower energy level (L) is 6, and if we ionize it, we remove the electron completely, so the value of U approaches infinity so 1/U becomes zero. Now we can substitute known values into the formula and we obtain: 1/w = 10967758(1/36 - 0) = (10967758)(0.02777777) = 304659. So if 1/w = 304659 waves per meter, w = 3.282 * 10**-6 meter, or 3.282 microns. That is the maximum wavelength of light that will ionize this atom, and it is in the infrared region.

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