Emission and absorption spectra Knowledge-Based Study

Study notes

1. The Nature of Optical Spectra

   When light from an illuminated source is dispersed through a prism or diffraction grating, it forms an ordered display of component wavelengths called a spectrum.

   Depending on the physical state and temperature of the source, spectra are classified into two broad categories:

   • Continuous Spectrum: An unbroken band of colors containing all wavelengths over a given range, produced by incandescent solids, liquids, or dense gases under high pressure (such as an incandescent lamp filament or the core of a star).
   • Line (Discrete) Spectrum: Distinct, isolated bright or dark spectral lines corresponding to specific, well-defined wavelengths. These are characteristic of isolated atoms or ions in low-density gases and vapors.

   Because every element possesses a unique nuclear charge and electronic structure, the wavelengths present in an atomic spectrum serve as an elemental fingerprint, enabling chemical identification through spectroscopy.

   Atomic Energy Quantization

   In modern physics, bound electrons within an atom occupy discrete, quantized energy states rather than a continuum of orbits. Transitions between these stationary states require the emission or absorption of a photon with an energy exactly matching the difference between the two states:

   $$\Delta E = |E_2 - E_1| = hf = \frac{hc}{\lambda}$$

   Here, $h$ represents Planck's constant, $f$ is the frequency of the radiation, $c$ is the speed of light in vacuum, and $\lambda$ is the spectral wavelength.

   De-excitation and Photon Emission

   When an electron in an excited state with energy $E_2$ drops to a lower state $E_1$, the atom releases the excess energy by emitting a single photon. Because the energy levels $E_1$ and $E_2$ are sharply defined, the emitted photon has a discrete frequency and wavelength, forming a bright line in an emission spectrum.

   Excitation and Photon Absorption

   Conversely, when a continuous spectrum of light passes through a gas, an electron in state $E_1$ can absorb a photon and jump to higher state $E_2$, provided the incident photon energy strictly equals $E_2 - E_1$. Photons with energies that do not match available transition differences pass through the gas without absorption.

   Distinguishing Emission and Absorption Spectra

   The observable appearance of an atomic spectrum depends directly on the experimental arrangement and the role of the gas:

   1. Line Emission Spectrum

   When a low-density gas is excited (e.g., via electrical discharge or thermal heating), its atoms transition downward from excited levels to lower levels. The emitted light, when viewed against a dark background through a spectroscope, appears as bright, narrow colored lines at characteristic wavelengths.

   2. Line Absorption Spectrum

   When white light containing a continuous range of wavelengths passes through a cool, low-density gas, the gas atoms absorb specifically those photon energies corresponding to their upward quantum transitions. These absorbed photons are subsequently re-emitted in all random directions. Consequently, the transmitted beam is depleted along the original line of sight, creating sharp dark lines across an otherwise continuous rainbow background.

   Kirchhoff's Spectroscopic Law

   Because the same pairs of energy levels are responsible for both processes, a gas absorbs light at the exact same wavelengths that it emits when heated. Famous examples include the Fraunhofer lines observed in the solar spectrum, where dark absorption lines reveal the elemental composition of the cooler outer layers (chromosphere) of the Sun.