SQA Advanced Higher Chemistry

Waves and photons

Electromagnetic radiation can be described as a wave, with a wavelength and a frequency, and it can also be described as a stream of particles called photons. This is its dual nature. The wave description accounts for how radiation travels and spreads out; the particle description is needed whenever radiation is absorbed or emitted by matter, because energy is then exchanged in whole photons and never in fractions of one.

The wavelength $\lambda$ is the distance between two adjacent crests and is measured in metres, although wavelengths of visible light are normally quoted in nanometres ($\pu{1 nm} = \pu{1e-9 m}$). The frequency $f$ is the number of waves passing a point each second, in hertz ($\pu{Hz} = \pu{s-1}$). All electromagnetic radiation travels at the same speed $c$ in a vacuum, about $\pu{3.00e8 m s-1}$, so wavelength and frequency are linked by

A longer wavelength therefore means a lower frequency. The electromagnetic spectrum is the full range of radiation arranged in order of wavelength. From the longest wavelength to the shortest it runs through radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Visible light covers roughly 400 nm (violet) to 700 nm (red).

Photon energy

A photon carries a quantised amount of energy that is proportional to the frequency of the radiation:

Here $E$ is the energy of one photon in joules, $h$ is Planck's constant ($\pu{6.63e-34 J s}$), $f$ is the frequency in $\pu{Hz}$ and $\lambda$ is the wavelength in metres. Because $E$ is proportional to $f$, the photons in high frequency radiation transfer more energy than the photons in low frequency radiation. An ultraviolet photon is more energetic than a photon of red light, which is why ultraviolet radiation is able to break bonds and damage skin.

Chemists usually want the energy for a mole of photons, found by multiplying by the Avogadro constant $L$ ($\pu{6.02e23 mol-1}$):

This is normally converted to $\pu{kJ mol-1}$, so that it can be compared with bond enthalpies and ionisation energies.

Worked example

Light of wavelength 520 nm is absorbed by a sample. Find the frequency, the energy of one photon and the energy of one mole of photons.

The energy per mole is about $\pu{231 kJ mol-1}$ (the small difference from 230 comes from rounding the intermediate values).

Energy levels and emission spectra

The electrons in an atom can only have certain fixed energies, so the atom has a set of discrete (quantised) energy levels. When energy is supplied, for example by heating or an electric discharge, an electron can be promoted from a lower energy level to a higher one. This excited state is unstable, and when the electron falls back to a lower level the atom emits a photon whose energy equals the difference between the two levels:

Since only certain energy differences are possible, only certain frequencies are emitted. The light from excited atoms therefore gives a line spectrum, a series of sharp lines at particular wavelengths on a dark background, and not a continuous band of colours. This is direct evidence that electrons in atoms occupy discrete energy levels. If energy levels were continuous, a continuous spectrum would be seen.

For example, if an electron in a hydrogen atom drops between two levels that are $\pu{3.03e-19 J}$ apart, the photon emitted has wavelength

which is a red line in the visible region.

Atomic absorption and emission spectroscopy

Every element has its own set of energy levels, and so its own characteristic emission and absorption spectra. The lines act like a fingerprint, and they can be used both to identify an element in a sample and to measure how much of it is present.

Emission spectroscopy

In emission spectroscopy a high temperature, such as that of a flame or a plasma, is used to excite the electrons in the atoms of the sample. As the electrons drop back to lower energy levels they emit photons. The instrument measures the intensity of the light emitted at different wavelengths to give an emission spectrum.

Absorption spectroscopy

In absorption spectroscopy the sample is first atomised, and electromagnetic radiation is directed at it. Photons whose energy exactly matches the gap between two energy levels are absorbed as electrons are promoted. The intensity of the light that comes through is measured across a range of wavelengths, and the absorption spectrum shows dark lines (missing wavelengths) on a bright background. The absorption lines of an element fall at the same wavelengths as its emission lines, because the same pairs of energy levels are involved.

Finding concentration

The wavelengths present show which elements are in the sample. The intensity of the light emitted or absorbed at a characteristic wavelength is related to the concentration of that element, so a sample can be compared against solutions of known concentration to measure how much of the element it contains.