The wave-particle nature of electromagnetic radiation, the relationships E = hf and c = f lambda, and how line emission and absorption spectra provide evidence for quantised electronic energy levels in atoms.

What this key area is asking

The SQA wants you to describe electromagnetic radiation as having a wave-particle nature, to use the relationships $E = hf$ and $c = f\lambda$ in calculations, and to explain how line emission and absorption spectra give evidence for quantised electronic energy levels in atoms. The calculation of photon energy and the link between spectral lines and energy gaps are reliable exam earners.

The wave-particle nature of light

The two pictures are complementary. Diffraction and interference show the wave behaviour, while the photoelectric effect and atomic spectra show the particle behaviour. The visible region is only a small part of the full spectrum, which runs from low-energy radio waves through microwave, infrared, visible and ultraviolet to high-energy X-rays and gamma rays.

Because $c$ is fixed, frequency and wavelength are inversely related: as wavelength decreases, frequency rises and so does the photon energy. Ultraviolet photons therefore carry far more energy than infrared photons.

Energy of a photon and a mole of photons

To find the energy associated with one mole of photons, multiply the single-photon energy by the Avogadro constant, $L = 6.02 \times 10^{23} \text{ mol}^{-1}$. This converts the tiny single-photon energy in joules into a molar energy in $\text{J mol}^{-1}$ that can be compared with bond enthalpies.

Line emission spectra

When an atom absorbs energy (from heat or an electric discharge), an electron is promoted to a higher energy level, leaving the atom in an excited state. The excited electron then falls back to a lower level, emitting a photon whose energy equals the difference between the two levels:

Each element has its own fingerprint of lines because its energy-level spacing is unique. This is the basis of flame tests and of atomic emission spectroscopy used to identify elements.

Line absorption spectra

An absorption spectrum is recorded by passing white light (a continuous spectrum) through a sample of gaseous atoms. Electrons absorb only those photons whose energy exactly matches an energy gap, so they are promoted to higher levels. The transmitted light is missing these frequencies, leaving dark lines at exactly the same positions as the bright lines of the emission spectrum.

The matching of emission and absorption lines confirms that the same energy gaps govern both processes. Astronomers use absorption lines in starlight to identify the elements present in stars.

Examples in context

Atomic spectra connect directly to analysis and to the wider world. Sodium street lamps glow orange because excited sodium atoms emit strongly at $589 \text{ nm}$, a single dominant emission line. Fireworks owe their colours to metal salts: strontium gives red, copper gives blue-green and barium gives green, each from a characteristic set of emission lines. In the laboratory, atomic emission and atomic absorption spectroscopy quantify trace metals in water and food by measuring the intensity of these element-specific lines. The same quantised-energy idea underpins the later spectroscopic techniques in this course, where photons of infrared, ultraviolet and radio frequency probe different energy transitions in molecules.

Try this

Q1. State the relationship between the energy of a photon and the frequency of the radiation. [1 mark]

• Cue. $E = hf$, where $h$ is the Planck constant.

Q2. Explain why each element produces a unique line emission spectrum. [2 marks]

• Cue. Each element has a unique set of energy-level spacings, so it emits a unique set of photon energies and therefore a unique set of lines.

Q3. Radiation has a frequency of $5.00 \times 10^{14} \text{ Hz}$. Calculate the energy of one photon. [1 mark]

• Cue. $E = hf = 6.63 \times 10^{-34} \times 5.00 \times 10^{14} = 3.32 \times 10^{-19} \text{ J}$.