To this end, we generate strong, time-dependent electric-field gradients, with which we apply forces on Rydberg atoms and molecules [ 1 ]. When the molecules are entrained in cold supersonic beams, the forces can be used to slow down the beams, the result being a slow beam of translationally cold atoms or molecules.

We call this deceleration technique Rydberg-Stark deceleration. It is a universal technique to generate cold atomic or molecular samples because all atoms and molecules have Rydberg states.

## Related items

Once trapped, the Rydberg atoms and molecules can be used in spectroscopic and collisional experiments, and to study the decay of Rydberg-atoms induced by blackbody radiation over long timescales [ 5 ]. Current work focuses on the deceleration and trapping of metastable 1s 2s 3 S 1 helium atom using a Rydberg-Stark decelerator and superimposed electric and magnetic traps.

Since triplet helium has a nonzero total electron spin, it interacts with magnetic fields. Once they decay from the Rydberg state back to the metastable state they remain confined in the magnetic trap. 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. You are familiar with prefixes like kilo meaning a thousand or 10 3 times , and mega meaning a million or 10 6 times.

## Rydberg molecule

Peta means 10 15 times. So a value like 3 PHz means 3 x 10 15 Hz. If you are worried about "Hertz", it just means "cycles per second". 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. 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.

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.

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. 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! You need to look at past papers and mark schemes. 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 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.

Three years later, Rydberg generalised this so that it was possible to work out the wavelengths of any of the lines in the hydrogen emission spectrum. In other words, if n 1 is, say, 2 then n 2 can be any whole number between 3 and infinity. 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.

In Balmer's equation, n 1 is always 2 - because that gives the wavelengths of the lines in the visible part of the spectrum which is what he was interested in. His original equation was also organised differently. The modern version shows more clearly what is going on. You can also use a modified version of the Rydberg equation to calculate the frequency of each of the lines. You can work out this version from the previous equation and the formula relating wavelength and frequency further up the page. Whichever version you use, the bigger number must always be the one at the bottom of the right-hand term - the one you take away.

If you get them the wrong way around, it is immediately obvious if you start to do a calculation, because you will end up with a negative answer!

### Publication details

The lines in the hydrogen emission spectrum form regular patterns and can be represented by a relatively simple equation. Each line can be calculated from a combination of simple whole numbers. 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. But if you supply energy to the atom, the electron gets excited into a higher energy level - or even removed from the atom altogether.

The high voltage in a discharge tube provides that energy. Hydrogen molecules are first broken up into hydrogen atoms hence the atomic hydrogen emission spectrum and electrons are then promoted into higher energy levels.

## Quantum dynamics of atomic and molecular systems

Suppose a particular electron was excited into the third energy level. This would tend to lose energy again by falling back down to a lower level.

It could do this in two different ways. 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. That energy which the electron loses comes out as light where "light" includes UV and IR as well as visible. If an electron falls from the 3-level to the 2-level, red light is seen.

This is the origin of the red line in the hydrogen spectrum. Calculate the wavelength of the lowest-energy line in the Lyman series to three significant figures. In what region of the electromagnetic spectrum does it occur?

Asked for: wavelength of the lowest-energy Lyman line and corresponding region of the spectrum. Spectroscopists often talk about energy and frequency as equivalent. The cm -1 unit wavenumbers is particularly convenient.

We can convert the answer in part A to cm This emission line is called Lyman alpha and is the strongest atomic emission line from the sun and drives the chemistry of the upper atmosphere of all the planets producing ions by stripping electrons from atoms and molecules. It is completely absorbed by oxygen in the upper stratosphere, dissociating O 2 molecules to O atoms which react with other O 2 molecules to form stratospheric ozone. B This wavelength is in the ultraviolet region of the spectrum.