Why is the helium spectrum have so many more lines than the hydrogen spectrum?

I take we are taking about the visible spectra (Balmer Series)? The two spectra have similar number of lines as below, although some are very feint. That a line apears in the visible spectrum will depend on the separation of the energy levels. We do not see transitions to level 1 for hydrogen or helium because the energy is too high and these appear in the UV. At the other end of the visible spectrum the Paschen series appear in the infrared.

Helium
wavelengths (nm)
438.793
443.755
447.148
471.314
492.193
501.567
504.774
587.562
667.815


Hydrogen (nm) transition
383.5384 9 -> 2 Violet
388.9049 8 -> 2 Violet
397.0072 7 -> 2 Violet
410.174 6 -> 2 Violet
434.047 5 -> 2 Violet
486.133 4 -> 2 Bluegreen (cyan)
656.272 3 -> 2 Red

The helium spectrum has more lines than the hydrogen spectrum because the two elements have different electron configurations and energy levels. To understand why helium has more lines in its spectrum, we need to consider the electron structure of both elements.

Helium (He) has two electrons, while hydrogen (H) only has one. The arrangement of electrons in an atom determines the energy levels and transitions, which in turn affect the emission or absorption of light.

In hydrogen, the electron is normally found in the first energy level (n=1). When the electron absorbs energy, it can transition to higher energy levels (such as n=2, n=3, etc.) and then release that energy as photons when it returns to a lower energy level. These transitions between energy levels give rise to the spectral lines observed in the hydrogen spectrum.

On the other hand, helium has two electrons. Each electron can occupy different energy levels and also interact with each other through electron-electron repulsion. This interaction leads to more complex energy level structures and more possible transitions between electron configurations. Thus, helium exhibits a more intricate spectrum with a greater number of lines.

To calculate the exact number of spectral lines in any element's spectrum, we can use the formula:

Number of spectral lines = (n^2 - n)/2,

where n represents the principal quantum number of the outermost electron. For hydrogen (with one electron), the formula simplifies to (n-1). For helium (with two electrons), it becomes more involved, taking into account both electron interactions and electron transitions between various energy levels.

In summary, the helium spectrum contains more lines than the hydrogen spectrum due to its more complex electron configuration and interactions between electrons, leading to a broader range of possible transitions and emission lines.