Introduction to Emission spectrum of hydrogen

When an electric discharge is passed through the hydrogen gas filled in the discharge tube at low pressure, light radiations are emitted by hydrogen. When these light radiations are passed through the prism, a spectrum consisting of bright lines known as Emission spectrum of hydrogen is obtained.

In 1884, J. J Balmer observed that there were four prominent coloured lines in the visible region of hydrogen spectrum. This series of four lines in the visible region was named as the Balmer Series. Later on, by careful observation four other spectral series were discovered in the infra-red and ultra-violet regions of hydrogen spectrum. These series were named after their discoverers. Thus, the Emission spectrum of hydrogen have five spectral series.

Name Region where located 1. Lyman Series 2. Balmer Series 3. Paschen Series 4. Brackett Series 5. Pfund Series Ultra-violet Visible Infra-red Infra-red Infra-red

Extending hydrogen's emission spectrum into the UV and IR

There is a lot more to the hydrogen spectrum than the three lines you can see with the naked eye. It is possible to detect patterns of lines in both the ultra-violet and infra-red regions of the spectrum as well.

These fall into a number of "series" of lines named after the person who discovered them. The diagram below shows three of these series, but there are others in the infra-red to the left of the Paschen series shown in the diagram.

The diagram is quite complicated, so we will look at it a bit at a time. Look first at the Lyman series on the right of the diagram - this is the most spread out one and easiest to see what is happening.

The Lyman series is a series of lines in the ultra-violet. Notice that the lines get closer and closer together as the frequency increases. Eventually, they get so close together that it becomes impossible to see them as anything other than a continuous spectrum. That's what the shaded bit on the right-hand end of the series suggests.

Then at one particular point, known as the series limit, the series stops.

If you now look at the Balmer series or the Paschen series, you will see that the pattern is just the same, but the series have become more compact. In the Balmer series, notice the position of the three visible lines from the photograph further up the page.

Complicating everything - frequency and wavelength

You will often find the hydrogen spectrum drawn using wavelengths of light rather than frequencies. Unfortunately, because of the mathematical relationship between the frequency of light and its wavelength, you get two completely different views of the spectrum if you plot it against frequency or against wavelength.

The relationship between frequency and wavelength

The mathematical relationship is:

Rearranging this gives equations for either wavelength or frequency.

What this means is that there is an inverse relationship between the two - a high frequency means a low wavelength and vice versa.

Drawing the hydrogen spectrum in terms of wavelength

This is what the spectrum looks like if you plot it in terms of wavelength instead of frequency:

. . . and just to remind you what the spectrum in terms of frequency looks like:

Is this confusing? Well, I find it extremely confusing! So what do you do about it?

For the rest of this page I shall only look at the spectrum plotted against frequency, because it is much easier to relate it to what is happening in the atom. Be aware that the spectrum looks different depending on how it is plotted, but, other than that, ignore the wavelength version unless it is obvious that your examiners want it. If you try to learn both versions, you are only going to get them muddled up!