what does the spectrum of hydrogen tell us about its electrons?

They are are allowed in only specific energy quanta.

well, first it only has one electron.

The spectrum gives you possible energy levels (states or orbit radius) for that electron.

the spectrum is the result of hydrogen's electron transitioning between energy levels

the levels are fixed
... quantized (per bob)

The spectrum of hydrogen provides valuable information about its electrons. When an electron in a hydrogen atom undergoes a transition from a higher energy level to a lower energy level, it releases energy in the form of light. This emitted light can be dispersed into different wavelengths, producing a spectrum.

The spectrum of hydrogen consists of a series of lines known as the hydrogen spectral lines. These lines correspond to specific transitions between different energy levels of the hydrogen atom. Each line is characterized by a unique wavelength or frequency.

The observation of the hydrogen spectrum led to the development of the Bohr model of the atom, proposed by Niels Bohr in 1913. According to the Bohr model, electrons in hydrogen occupy specific quantized energy levels. When an electron transitions from a higher energy level to a lower energy level, it emits a photon with energy equal to the difference in energy between the two levels. This energy difference determines the wavelength or frequency of the emitted light.

Therefore, by studying the hydrogen spectrum, scientists can determine the energy levels and transitions that the electrons in hydrogen undergo. This understanding of the electron energy levels in hydrogen has broader implications and provides the foundation for our understanding of atomic structure and the behavior of electrons in other atoms and molecules.