What wavelength of light is emitted when an electron drops from the third orbital (n = 3) to the ground state (n = 1) of hydrogen? Use the Rydberg constant R = 1.097 x 10^7 per metre.

1. The Rydberg formula is 1 divided by wavelength equals R times (1 divided by nf squared minus 1 divided by ni squared). 2. Substitute nf = 1 and ni = 3: 1 divided by wavelength = (1.097 x 10^7)(1 minus 1/9). 3. Evaluating the bracket gives about 0.889, so 1 divided by wavelength equals about 9.75 x 10^6 per metre. 4. Taking the reciprocal gives a wavelength of about 1.026 x 10^-7 m, which is 102.6 nm. 5. 51.3 nm is half this value, and 205.2 and 410.4 nm are two and four times too large. 6. So 102.6 nm is correct. _Source: OpenStax Physics (CC BY 4.0), Ch 22 "The Atom", section 22.1 The Structure of the Atom_