Electromagnetic radiation and atomic spectra are key to understanding how atoms interact with light. This topic dives into the properties of light waves and how they relate to electron transitions in atoms.

We'll explore how atoms emit and absorb specific colors of light, creating unique spectral patterns. These patterns help identify elements and reveal the inner workings of atomic structure.

Electromagnetic Spectrum and Atomic Transitions

Properties and Characteristics of Electromagnetic Radiation

• The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation, from low frequency radio waves to high frequency gamma rays
  • Different regions of the spectrum have different wavelengths and energies (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays)
• Electromagnetic radiation is produced when an electric charge accelerates or decelerates
  • In atoms, this occurs when electrons transition between different energy levels
• The energy of a photon of electromagnetic radiation is directly proportional to its frequency and inversely proportional to its wavelength
  • Described by the equation $E = hν = hc/λ$, where $h$ is Planck's constant, $ν$ is the frequency, $c$ is the speed of light, and $λ$ is the wavelength

Relationship between Atomic Transitions and the Electromagnetic Spectrum

• Atomic transitions between different energy levels result in the emission or absorption of photons with specific frequencies and wavelengths, corresponding to specific regions of the electromagnetic spectrum
  • Example: Hydrogen atom transitions in the Balmer series emit photons in the visible light region
• The Bohr model of the atom explains the relationship between atomic transitions and the electromagnetic spectrum
  • Electrons can only occupy discrete energy levels
  • Transitions between these levels result in the emission or absorption of photons with specific energies
  • Energy differences between levels determine the wavelengths and frequencies of emitted or absorbed photons

Atomic Emission and Absorption Spectra

Origin of Atomic Emission Spectra

• Atomic emission spectra are produced when electrons in excited atoms transition from higher energy levels to lower energy levels
  • Electrons release photons with specific energies and wavelengths during these transitions
• The specific wavelengths of light emitted by an atom depend on the energy differences between the atom's allowed electron energy levels
  • These energy differences are unique to each element, resulting in characteristic emission spectra
• The Bohr model explains the origin of emission spectra by proposing that electrons can only occupy discrete energy levels and that transitions between these levels result in the emission of photons with specific energies

Origin of Atomic Absorption Spectra

• Atomic absorption spectra are produced when electrons in atoms absorb photons with specific energies and wavelengths
  • Electrons transition from lower energy levels to higher energy levels during absorption
• The specific wavelengths of light absorbed by an atom depend on the energy differences between the atom's allowed electron energy levels
  • These energy differences are unique to each element, resulting in characteristic absorption spectra
• The energy of a photon absorbed during an atomic transition is equal to the difference in energy between the initial and final electron energy levels
  • Described by the equation $ΔE = E_f - E_i = hν$, where $ΔE$ is the energy difference, $E_f$ and $E_i$ are the final and initial electron energy levels, $h$ is Planck's constant, and $ν$ is the frequency of the photon

Structure of Atomic Spectra

Characteristics of Spectral Lines

• Atomic spectra consist of a series of discrete spectral lines, each corresponding to a specific electron transition between energy levels
• Emission spectra show bright spectral lines on a dark background, while absorption spectra show dark spectral lines on a bright background
• The wavelengths and frequencies of spectral lines are unique to each element, serving as a "fingerprint" for identifying the presence of specific elements in a sample
  • Example: Sodium emission spectrum shows characteristic yellow lines at 589.0 nm and 589.6 nm

Factors Influencing Spectral Lines

• The intensity of spectral lines depends on factors such as:
  • Population of electrons in the initial energy level
  • Transition probability
  • Temperature of the sample
• The width of spectral lines is influenced by various factors:
  • Natural linewidth (due to the uncertainty principle)
  • Doppler broadening (due to the motion of atoms)
  • Pressure broadening (due to collisions between atoms)
• Spectral lines in atomic spectra can be grouped into series based on the energy levels involved in the transitions
  • Example: Lyman, Balmer, Paschen, and Brackett series in the hydrogen atom

Bohr Model for Energy Levels and Transitions

Calculating Energy Levels using the Bohr Model

• The Bohr model of the atom proposes that electrons can only occupy discrete energy levels
  • The energy of an electron in a particular level is given by the equation $E_n = -13.6 \text{ eV} / n^2$, where $E_n$ is the energy of the $n$th level and $n$ is the principal quantum number ($n = 1, 2, 3, ...$)
• The energy difference between two electron energy levels can be calculated using the equation $ΔE = E_f - E_i = -13.6 \text{ eV} (1/n_f^2 - 1/n_i^2)$, where $ΔE$ is the energy difference, $E_f$ and $E_i$ are the final and initial electron energy levels, and $n_f$ and $n_i$ are the principal quantum numbers of the final and initial levels

Determining Transition Frequencies and Wavelengths

• The frequency and wavelength of a photon emitted or absorbed during an atomic transition can be calculated using the equations:
  • Frequency: $ν = ΔE / h$
  • Wavelength: $λ = hc / ΔE$
  • where $ν$ is the frequency, $λ$ is the wavelength, $ΔE$ is the energy difference between the initial and final electron energy levels, $h$ is Planck's constant, and $c$ is the speed of light
• The Rydberg formula can be used to calculate the wavelengths of spectral lines in the hydrogen atom:
  • $1/λ = R (1/n_f^2 - 1/n_i^2)$, where $λ$ is the wavelength, $R$ is the Rydberg constant, and $n_f$ and $n_i$ are the principal quantum numbers of the final and initial energy levels
• The Bohr model can explain the general structure of atomic spectra and the origin of spectral lines, but it has limitations
  • Unable to accurately describe multi-electron atoms or the fine structure of spectral lines
  • Quantum mechanics provides a more comprehensive description of atomic structure and spectra