2.2.5

# Energy Levels & Photon Emission

Test yourself

## Energy Levels in Atoms

Electrons in atoms must occupy a discrete energy level.

### Energy levels

• Electrons do not float around randomly in atoms.
• They can only be found at set energy levels.
• Each energy level is given a 'quantum number'.
• The ground state is the lowest energy level. The ground state has n = 1.
• The higher the energy level, the larger its quantum number, n.

### Transitions between energy levels

• An electron can transition between energy levels by absorbing or emitting a photon of a specific frequency.
• If an electron emits a photon, it will drop an energy level.
• If an electron absorbs a photon, it will rise to a higher level.
• In both cases, the photon must have energy exactly equal to the energy difference between the levels.

### Equation

• The movement of electrons between energy levels can be represented in the equation:
• $\Delta E = E_2 - E_1 = hf = \frac{hc}{\lambda}$
• This shows that the energy difference between levels one and two is equal to the energy of the emitted (or absorbed) photon.

### Excitation and ionisation

• If an electron absorbs a photon and jumps up an energy level, we say it has been excited.
• If an electron absorbs a photon that is so energetic it is knocked out of the atom altogether, the electron has been ionised.

## Absorption Spectra

Electrons in atoms can only move between discrete energy levels. So an atom can only absorb or emit photons with particular frequencies (or wavelengths).

### White light - continuous spectrum

• White light contains all the colours in the visible part of the spectrum.
• When white light is passed through a prism or a diffraction grating, the colours are split up to produce a continuous spectrum.
• Continuous means there aren't any gaps or black lines.

### Cool gas - absorption spectra

• A cool gas means a gas containing atoms in their ground state.
• When white light is passed through a cool gas, electrons in the ground state of the atom absorb certain frequencies of light and become excited.
• Most frequencies of the white light are not absorbed because they do not correspond to the difference between two energy levels in the atom.

### Absorption spectra 2

• If the light coming out of the cool gas is split by a prism (or diffraction grating), we see a continuous spectrum with black lines.
• These lines are called absorption lines.
• They are unique to each type of atom.

## Emission Spectra

Electrons in atoms can only move between discrete energy levels. So an atom can only absorb or emit photons with particular frequencies (or wavelengths).

### Excited gas

• An excited gas contains atoms in excited energy states.
• These excited atoms contain electrons in high energy levels.
• As these electrons de-excite and fall back to lower energy levels, photons are emitted.

### Photon emission

• These photons carry away energy from the atoms.
• The amount of energy (and so what frequency) the photons have depends on the difference in energy levels in the atom.
• For every possible electron transition, there will be a unique frequency photon emitted.
• We see a series of bright lines when we pass the emitted light through a prism or diffraction grating.

### Emission vs absorption

• Compare the emission and absorption spectra produced by this gas.
• We can see that the emission lines exactly match the frequencies of the absorption lines.
• This is because the lines correspond to the same energy differences in the atoms. The same energy photons are either emitted or absorbed.