1.1 Nature of light and electromagnetic spectrum

Light exhibits a dual nature: it behaves as both a wave and a particle. This duality is the foundation of photochemistry, explaining everything from interference patterns to the photoelectric effect. Understanding how light carries and delivers energy to molecules is essential before diving into any photochemical process.

The electromagnetic spectrum stretches from low-energy radio waves to high-energy gamma rays, but photochemistry focuses primarily on the narrow visible band (380–750 nm) and nearby UV region. These wavelengths carry enough energy to excite electrons in molecules, driving reactions like photosynthesis, vision, and photocatalysis.

Electromagnetic Radiation and Light

Wave-particle duality of light

Light doesn't fit neatly into one category. Sometimes it behaves like a wave, sometimes like a stream of particles. Both descriptions are correct, and you need both to fully explain how light interacts with matter.

Wave behavior shows up in phenomena you can observe directly:

• Interference — in the double-slit experiment, light passing through two narrow slits creates alternating bright and dark bands on a screen, just as overlapping water waves reinforce or cancel each other
• Diffraction — light bends around obstacles or spreads after passing through a narrow opening
• Refraction — light changes speed and direction when moving between media (e.g., air to glass), which is why a straw looks bent in water

Particle behavior appears when light interacts with matter at the quantum level:

• Photoelectric effect — light striking a metal surface ejects electrons, but only if the light's frequency exceeds a threshold. Increasing intensity (brightness) alone won't work if the frequency is too low. This was the observation Einstein explained by proposing that light comes in discrete energy packets called photons.
• Compton scattering — X-ray photons collide with electrons and lose energy, shifting to longer wavelengths, exactly as you'd expect from a particle collision.

Each photon carries a specific amount of energy given by:

$E = h\nu$

where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s) and $\nu$ is the frequency of the light.

Historical progression: Classical physics treated light purely as a wave, described by Maxwell's electromagnetic equations (1860s). Planck introduced energy quantization in 1900 to explain blackbody radiation, and Einstein extended this in 1905 by proposing that light itself is quantized into photons. Together, these ideas launched quantum theory.

Regions of the electromagnetic spectrum

The electromagnetic spectrum is a continuum of radiation organized by wavelength (or equivalently, frequency and energy). Here are the major regions, from lowest to highest energy:

For photochemistry, the visible and UV regions matter most. These photons have enough energy (roughly 1.5–6 eV) to promote electrons into higher-energy molecular orbitals, which is the first step in any photochemical reaction.

Wavelength, frequency, and energy relationships

Three equations tie together the key properties of light. They're worth knowing cold.

1. Speed of light equation: $c = \lambda \nu$

   This says the speed of light ($c = 3.00 \times 10^{8}$ m/s in vacuum) equals wavelength times frequency. Since $c$ is constant, wavelength and frequency are inversely related: longer wavelength means lower frequency, and vice versa.

2. Photon energy: $E = h\nu$

   Energy is directly proportional to frequency. Higher frequency means more energy per photon.

3. Combining the two: $E = \frac{hc}{\lambda}$

   Substituting $\nu = \frac{c}{\lambda}$ into the energy equation gives you energy in terms of wavelength. Energy is inversely proportional to wavelength: shorter wavelengths pack more energy.

Quick summary of relationships:

• Wavelength ↑ → Frequency ↓ → Energy ↓ (radio waves: long wavelength, low energy)
• Wavelength ↓ → Frequency ↑ → Energy ↑ (gamma rays: short wavelength, high energy)

Example calculation: What's the energy of a green photon at 520 nm?

$E = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{520 \times 10^{-9}} = 3.82 \times 10^{-19} \text{ J} \approx 2.39 \text{ eV}$

That 2.39 eV is enough to trigger electronic transitions in many organic chromophores.

Visible light in photochemistry

The visible spectrum (380–750 nm) is a small slice of the electromagnetic spectrum, but it's where most photochemistry happens. The approximate color breakdown:

• Violet: 380–450 nm
• Blue: 450–495 nm
• Green: 495–570 nm
• Yellow: 570–590 nm
• Orange: 590–620 nm
• Red: 620–750 nm

When a molecule absorbs a visible photon, the energy promotes an electron from a lower-energy orbital to a higher one. This is called an electronic transition, and it occurs in the part of the molecule known as the chromophore (the light-absorbing group).

Several major processes depend on visible-light absorption:

• Photosynthesis — Chlorophyll absorbs strongly in the red (~680 nm) and blue (~430 nm) regions, which is why plants appear green (they reflect green light). The absorbed energy drives the conversion of $CO_2$ and $H_2O$ into glucose.
• Vision — The protein rhodopsin in your retinal cells contains a chromophore called retinal. When retinal absorbs a photon, it undergoes photoisomerization (a light-driven shape change from cis to trans), triggering a nerve signal to the brain.
• Photocatalysis — Materials like titanium dioxide ($TiO_2$) absorb light and generate reactive species on their surfaces, useful for breaking down pollutants or splitting water.
• Photovoltaics — Solar cells absorb visible photons to generate electrical current. Solar radiation peaks in the visible range, which is why this region is so important for energy applications.

Analytical techniques also rely on visible light. UV-Vis spectroscopy measures which wavelengths a sample absorbs, revealing information about electronic structure and concentration. Fluorescence spectroscopy detects light that molecules re-emit after absorbing photons, useful for identifying and quantifying specific compounds.