Atomic spectra UV and quantized electronic energy
Atomic spectra UV refers to ultraviolet line spectra produced when atoms absorb or emit photons during electronic transitions between quantized energy levels. Because UV wavelengths are short, the associated photon energies are relatively large, matching transitions that involve sizeable gaps between atomic energy levels.
A line in an atomic spectrum corresponds to one photon energy: \(E = h \cdot f = \dfrac{h \cdot c}{\lambda}\). Shorter wavelength \(\lambda\) implies larger photon energy \(E\), placing many strong “resonance” transitions in the ultraviolet.
Why ultraviolet lines are common in atomic spectra
- Discrete levels: isolated atoms have quantized electronic energies, so spectra consist of lines rather than broad bands.
- Large level spacings near the ground state: transitions involving the ground state typically have higher energy, often falling in the UV.
- Nuclear charge effects: hydrogen-like energies scale approximately with \(Z^2\), increasing transition energies and shifting lines toward shorter wavelengths.
- Atomic vs molecular spectra: atomic spectra UV lines are sharp; molecular UV–Vis features are often bands due to vibrational and rotational structure.
Hydrogen-like model and the UV (Lyman) series
For hydrogen-like atoms (one electron), the allowed transition wavelengths follow the Rydberg relation:
\[ \frac{1}{\lambda} = R \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right), \quad n_2 > n_1, \]where \(R\) is the Rydberg constant (approximately \(1.097 \times 10^{7}\ \mathrm{m^{-1}}\) for hydrogen). Ultraviolet lines for hydrogen arise prominently from the Lyman series, defined by \(n_1 = 1\).
Numerical example for an atomic spectra UV line (hydrogen Lyman-\(\alpha\))
The Lyman-\(\alpha\) line corresponds to the transition \(n_2 = 2 \rightarrow n_1 = 1\).
\[ \frac{1}{\lambda} = R \left(1 - \frac{1}{2^2}\right) = R \left(\frac{3}{4}\right) \quad \Rightarrow \quad \lambda = \frac{1}{\left(\frac{3}{4}\right) \cdot R} \]Using \(R = 1.097 \times 10^{7}\ \mathrm{m^{-1}}\):
\[ \lambda = \frac{1}{0.75 \cdot 1.097 \times 10^{7}}\ \mathrm{m} \approx 1.216 \times 10^{-7}\ \mathrm{m} = 121.6\ \mathrm{nm} \]The photon energy for \(\lambda = 121.6\ \mathrm{nm}\) follows \(E = \dfrac{h \cdot c}{\lambda}\), with \(h = 6.62607015 \times 10^{-34}\ \mathrm{J \cdot s}\) and \(c = 2.99792458 \times 10^{8}\ \mathrm{m \cdot s^{-1}}\).
\[ E = \frac{(6.62607015 \times 10^{-34}) \cdot (2.99792458 \times 10^{8})}{1.216 \times 10^{-7}}\ \mathrm{J} \approx 1.63 \times 10^{-18}\ \mathrm{J} \] \[ E \approx \frac{1.63 \times 10^{-18}}{1.602176634 \times 10^{-19}}\ \mathrm{eV} \approx 10.2\ \mathrm{eV} \]Representative UV lines in the Lyman series
Several transitions ending at \(n_1 = 1\) illustrate the ultraviolet character of atomic spectra UV for hydrogen.
| Transition | Rydberg form | Approx. wavelength (nm) | Region |
|---|---|---|---|
| \(2 \rightarrow 1\) | \(\dfrac{1}{\lambda} = R \left(1 - \dfrac{1}{4}\right)\) | 121.6 | UV |
| \(3 \rightarrow 1\) | \(\dfrac{1}{\lambda} = R \left(1 - \dfrac{1}{9}\right)\) | 102.6 | UV |
| \(4 \rightarrow 1\) | \(\dfrac{1}{\lambda} = R \left(1 - \dfrac{1}{16}\right)\) | 97.2 | UV |
| \(\infty \rightarrow 1\) (series limit) | \(\dfrac{1}{\lambda} = R\) | 91.2 | Far UV |
Connections to UV spectroscopy in general chemistry
Atomic emission and atomic absorption
Atomic emission spectra arise when excited atoms relax and emit photons at discrete wavelengths. Atomic absorption uses the same discrete energies: ground-state atoms absorb photons whose energies match allowed transitions, commonly in the UV for many elements because resonance transitions are high-energy.
Practical wavelength regions
The ultraviolet region spans roughly \(10\ \mathrm{nm}\) to \(400\ \mathrm{nm}\). Many laboratory UV measurements focus on near-UV (approximately \(200\ \mathrm{nm}\) to \(400\ \mathrm{nm}\)) because air and common glass strongly attenuate deeper UV, whereas quartz optics transmit further into the UV.
Common pitfalls
- Line spectra vs bands: atomic spectra UV lines are narrow; molecular UV–Vis spectra often show broad bands from vibronic structure and solvent effects.
- Continuum radiation vs characteristic lines: thermal sources can produce continuous spectra, while atomic line spectra reflect specific electronic transitions.
- Wavelength–energy intuition: a decrease in \(\lambda\) implies an increase in \(E\) because \(E = h \cdot c / \lambda\).
Summary statement
Atomic spectra UV originates from electronic transitions with relatively large energy differences, especially transitions involving the ground state; the ultraviolet wavelengths follow directly from the photon relation \(E = h \cdot c / \lambda\) and, for hydrogen-like systems, the Rydberg equation linking \(\lambda\) to \((n_1, n_2)\).