Question

How can the single electron in a hydrogen atom produce all of the lines found in its emission spectrum

Answer 1

The energy levels in the Hydrogen atom shows all the possible wavelengths from various energy differences in the atom.
You may be looking at the absorption spectrum. Hydrogen only produces the missing wavelengths in the image. They correspond to jumps between electron energy levels.

Answer 2

Hydrogen has a single electron but the atom has many shells.

Hydrogen is the first element that we encounter in the periodic table. It contains only one electron.

For convenience, most periodic tables place hydrogen as the first element in group one.

Even though it has one electron, there are many accessible shells. Spectral lines are produced when an electron moves from one of these accessible shells to another.

Hence, the single electron in hydrogen atom produces all the spectral lines found in its spectrum by transition from one energy level to another.

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