 # Electron Energy Levels

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## Electron Energy Levels

#### Introduction

The Sun should produce pure white light i.e. light from every frequency should be present. But study the spectrum produced by the Sun and you get gaps (lines) on it where light of particular frequencies is missing.

Why? The light leaving the Sun has to pass through gas clouds at the surface of the Sun. All the photons of a particular frequency (and therefore of a particular energy) are absorbed by the gas. In fact, they are absorbed by electrons in the gas atoms.

Why are only set frequencies absorbed? The reason for this is that electrons can only exist in atoms in certain energy states (or levels). Like books on a bookshelf, you can't have electrons half way between one level and the next.

To move from one level to the next requires set amounts of energy. Photons with these amounts of energy are the ones absorbed by the gas. Other photons, with more or less energy than these values, are left untouched. Hence you get lines (which are gaps) on the spectrum where photons are missing.

We draw energy level diagrams like this: If each level has an energy value, it is easy to see that the difference between the energy levels must equal the energy delivered by the photon.

hf = E1 - E2

Where

E1 = the energy needed to be at level 1

E2 = the energy needed to be at level 2. Note that there is an alternative method to exciting electrons. If you hit them with other electrons, they can gain just the right amount of energy from the collision to make the jump!

#### Why are the energy levels given negative values?

The concept here is repeated in the sections on gravitational and electric fields.

Consider an electron and the nucleus of an atom. They attract each other due to their opposite charge. As a result of this attraction the electron has potential energy, Ep.

As the electron moves away from the nucleus, this potential energy increases (in the same way as the potential energy of a stone increases as it moves away from the surface of the Earth). However, as the electron moves away from the nucleus, the increased distance makes the force due to the electrical attraction smaller. At infinity, the attraction between the two is zero. No attraction - no potential energy.

So at the biggest distance from the nucleus, where you would logically expect to have the biggest value of potential energy, you find that the Ep value is in fact zero. Doh!! That means that the biggest value possible is zero. Therefore, as you move back towards the nucleus and lose potential energy, you must be going below zero potential energy, i.e. you must have negative potential energy.

For this reason, all the electron energy levels in diagrams are given a negative value, showing that the potential energy at that point is less than it is at infinity.

#### So what do the electrons do once they are excited?

Electrons are rather middle aged in this regard. They don't really like being excited. Consequently, very shortly after becoming excited they drop back to the lower energy state. Of course that means that they have to lose some energy and to do this they give out a packet of energy - a photon. The size of the photon equals the size of the jump that they have to make. So once again you can calculate the expected frequency of the emitted photon using

hf = E1- E2

The more energetic the jumps (up or down) the higher the frequency of the photon absorbed or emitted so the further into the U-V end of the spectrum the lines go.

#### Absorption and emission spectra

Because each atom has a different electron structure, each element can be identified by the photons that it absorbs or emits from its electrons moving from energy level to energy level.

Single atoms give out the clearest results when you examine the spectra for different elements. That's because when they are involved in bonding with other atoms, the electrons feel influences from places other than just the atom itself. That distorts the results. So to get the best results we use gas at low pressure in vapour tubes.

The absorption spectrum

Shine white light through vapour of a particular element. Analyse the spectrum of the light that has passed through the vapour. It has gaps in what is otherwise a perfect spectrum. That's an absorption spectrum.

The emission spectrum

Excite electrons in a vapour. (Remember that you can do this in two ways. Either use photons or use other electrons.) Collect the photons that are emitted when the electrons drop from the higher energy levels down to the lower levels.

This will produce a series of coloured lines on a mainly black background - showing that light is only emitted at certain frequencies relating to certain jumps.

That's an emission spectrum.

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