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This page introduces the atomic hydrogen emission spectrum, showing how it arises from electron movements between energy levels within the atom.
A hydrogen discharge tube is a slim tube containing hydrogen gas at low pressure with an electrode at each end. If the light is passed through a prism or diffraction grating, it is split into its various colours. The photograph shows part of a hydrogen discharge tube on the left, and the three most easily seen lines in the visible part of the spectrum on the right. There is a lot more to the hydrogen spectrum than the three lines you can see with the naked eye. 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. You will often find the hydrogen spectrum drawn using wavelengths of light rather than frequencies.
What this means is that there is an inverse relationship between the two - a high frequency means a low wavelength and vice versa. 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.
If you are working towards a UK-based exam and don't have these things, you can find out how to get hold of them by going to the syllabuses page. By an amazing bit of mathematical insight, in 1885 Balmer came up with a simple formula for predicting the wavelength of any of the lines in what we now know as the Balmer series.
The various combinations of numbers that you can slot into this formula let you calculate the wavelength of any of the lines in the hydrogen emission spectrum - and there is close agreement between the wavelengths that you get using this formula and those found by analysing a real spectrum.
You can also use a modified version of the Rydberg equation to calculate the frequency of each of the lines. The lines in the hydrogen emission spectrum form regular patterns and can be represented by a (relatively) simple equation.
Why does hydrogen emit light when it is excited by being exposed to a high voltage and what is the significance of those whole numbers? When nothing is exciting it, hydrogen's electron is in the first energy level - the level closest to the nucleus.
It could fall all the way back down to the first level again, or it could fall back to the second level - and then, in a second jump, down to the first level.
If an electron falls from the 3-level to the 2-level, it has to lose an amount of energy exactly the same as the energy gap between those two levels.

The last equation can therefore be re-written as a measure of the energy gap between two electron levels.
The greatest possible fall in energy will therefore produce the highest frequency line in the spectrum. The next few diagrams are in two parts - with the energy levels at the top and the spectrum at the bottom. If an electron fell from the 6-level, the fall is a little bit less, and so the frequency will be a little bit lower. If you do the same thing for jumps down to the 2-level, you end up with the lines in the Balmer series. The Paschen series would be produced by jumps down to the 3-level, but the diagram is going to get very messy if I include those as well - not to mention all the other series with jumps down to the 4-level, the 5-level and so on.
The infinity level represents the highest possible energy an electron can have as a part of a hydrogen atom. When there is no additional energy supplied to it, hydrogen's electron is found at the 1-level. The ionisation energy per electron is therefore a measure of the distance between the 1-level and the infinity level.
If you can determine the frequency of the Lyman series limit, you can use it to calculate the energy needed to move the electron in one atom from the 1-level to the point of ionisation. The problem is that the frequency of a series limit is quite difficult to find accurately from a spectrum because the lines are so close together in that region that the spectrum looks continuous. Here is a list of the frequencies of the seven most widely spaced lines in the Lyman series, together with the increase in frequency as you go from one to the next. That means that if you were to plot the increases in frequency against the actual frequency, you could extrapolate (continue) the curve to the point at which the increase becomes zero.
It doesn't matter, as long as you are always consistent - in other words, as long as you always plot the difference against either the higher or the lower figure. As you will see from the graph below, by plotting both of the possible curves on the same graph, it makes it easier to decide exactly how to extrapolate the curves. We can work out the energy gap between the ground state and the point at which the electron leaves the atom by substituting the value we've got for frequency and looking up the value of Planck's constant from a data book. This compares well with the normally quoted value for hydrogen's ionisation energy of 1312 kJ mol-1. If this is the first set of questions you have done, please read the introductory page before you start.

After you click in the first animation, the sentence will seem to read, “When wave speed was held constant, the frequency of the sound increased.” While a sentence like that is written in perfectly good academic language, it seems to infer that holding the wave speed constant caused the frequency of the sound to increase. Younger students may be able to better grasp this concept if it is more general – replacing “doubled” with increased and calling it simply a direct relationship.
Younger students may be able to better grasp this concept if it is more general – replacing “doubled” and “halved” with “increased” and “decreased” and calling it simply an inverse relationship. Cause and EffectWhen wave speed was held constant… The wavelength of The frequency the vibrating string of the sound was shortened. Cause and EffectWhen wavelength was held constant… The frequency The speed of the of the sound wave decreased.
Cause and Effect Relationships• Using academic language, describe the cause and effect relationship between:1. Mathematical Relationships• The formula that relates wave speed, wavelength and frequency is: • V= f x ?• In the next few slides, we’ll look at some mathematical relationships between these variables. V=f x ?• If wavelength is held constant and frequency is doubled, what happens to wave speed (velocity)? V=f x ?• If wave speed is held constant and frequency is doubled, what happens to wavelength?
Mathematical Relationships• Using mathematical reasoning and language, create a mathematical example that describes the cause and effect relationship between:1. This is a great time to point this out to students and prompt them to think about whether or not holding wave speed constant is really a “cause” or if it is simply a condition. This is an intentional effort to: 1) encourage students to use their notes 2) encourage students to think for themselves. As I teach ELA and special education 9th graders, I often give my students some choices to use when constructing an academic language sentence. In this cause and effect assignment, I would put words up on the board such as: because, because of, as a result, caused, led to, resulted in, if…then…, due to, etc.