What have we learned since Bohr proposed his model of hydrogen?

The Bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $\text{He}^+$He​+​​H, e, start superscript, plus, end superscript. Unfortunately, it did not do as well when applied to the spectra of more complex atoms. Furthermore, the Bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the Zeeman effect.

In the following decades, work by scientists such as Erwin Schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles. This means that it is not possible to know both a given electron’s position in space and its velocity at the same time, a concept that is more precisely stated in Heisenberg's uncertainty principle. The uncertainty principle contradicts Bohr’s idea of electrons existing in specific orbits with a known velocity and radius. Instead, we can only calculate probabilities of finding electrons in a particular region of space around the nucleus.

The modern quantum mechanical model may sound like a huge leap from the Bohr model, but the key idea is the same: classical physics is not sufficient to explain all phenomena on an atomic level. Bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom, and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems.