Introduction to Spectroscopy – Core Concepts

Electromagnetic Spectrum & Energy

• EMR ranges from radio waves to gamma rays (long $\lambda$, low $v$ → short $\lambda$, high $v$).
• Energy increases with frequency: cosmic > $\gamma$ > X-ray > UV > visible > IR > microwave > radio.
• Visible region ≈ $400{-}700\,\text{nm}$ (violet → red).
• Longer $\lambda$ (e.g., $740\,\text{nm}$) = lower energy than shorter $\lambda$ (e.g., $470\,\text{nm}$).

Wave Properties of EMR

• Characterised by:
  • Wavelength $\lambda$ = distance between successive maxima/minima.
  • Frequency $v$ (Hz) = oscillations · s$^{-1}$.
  • Amplitude = field strength at crest.
• Relationship: $v \lambda = c$ where c \approx 3.00 \times 10^{8}\,\text{m·s}^{-1}.
• High $v$ ⇔ short $\lambda$; low $v$ ⇔ long $\lambda$.
• Interference:
  • Constructive = waves reinforce.
  • Destructive = waves cancel.
  • Monochromatic = single $v$; Polychromatic = multiple $v$.

Quantum (Photon) Model

• Wave description fails for absorption/emission → use photons (quanta).
• Photon energy: $E = h v$, with h = 6.624 \times 10^{-34}\,\text{J·s}.
• High-energy photons = high $v$ / short $\lambda$.

Key Equations

• Wave: $v \lambda = c$
• Planck: $E = h v$
• Combined: $E = \dfrac{h c}{\lambda}$ (energy ∝ $1/\lambda$).

Wavenumber

• Defined: $\tilde{v} = \dfrac{1}{\lambda}$ (usually cm$^{-1}$).
• Energy form: $E = h c \tilde{v}$ (energy ∝ wavenumber).

Interaction of EMR with Matter

• Major processes: absorption, emission, scattering, refraction, diffraction.

Absorption / Emission

• Absorption: matter takes EMR; occurs at discrete energies.
• Emission: excited matter releases photons.
• Energy change: $\Delta E = h v$.

Scattering

• Rayleigh: elastic (no $\Delta E$).
• Raman (Stokes/Anti-Stokes): inelastic (energy shift relative to Rayleigh).

Refraction

• Change in light direction at interface; governed by Snell’s law (due to velocity change).
• Always accompanied by some reflection.

Diffraction

• Bending of light around edges/openings.
• Diffraction gratings precisely separate frequencies; core component in spectrometers.

Spectrometers

• Instruments measuring EMR–matter interactions; axis choice (e.g., $\lambda$, $v$, $\tilde{v}$, $E$) depends on technique.