Spectroscopy and Atomic Structure - Flashcards

Spectroscopy and Atomic Structure — Study Notes (Ch. 4)

Fundamentals of Spectroscopy

• Spectroscopy studies how matter interacts with electromagnetic radiation to reveal composition, motion, temperature, and physical conditions.
• Wave concepts from the transcript:
  • Undisturbed state, amplitude, and direction of wave motion are key descriptors of a wave.
  • Observations depend on whether the source is at rest or moving relative to the observer (Doppler effects discussed later).
• Intensity and frequency:
  • Intensity relates to the brightness/strength of the light.
  • The arrow in the lecture figures indicates the frequency of peak emission; higher intensity can correspond to different peak wavelengths depending on temperature and source characteristics.
• Observations of motion:
  • Moving source alters the observed wavelength (and thus color) of emitted light due to Doppler effects; the setup shows successive wave crests emitted from a moving source reaching the observer at different times, altering the measured wavelength.

Temperature and Stellar Radiation

• Wien’s Law (displacement law):
  • The peak emission wavelength of a blackbody is inversely proportional to its temperature:
  • \lambda_{\text{max}} T = b, \quad b \approx 2.898 \times 10^{-3} \ \text{m K}.
  • Higher temperature -> shorter peak wavelength (bluer color); lower temperature -> longer peak wavelength (redder color).
• Stefan–Boltzmann Law (total power radiated):
  • The total emitted power per unit area is proportional to the fourth power of temperature:
  • j^* = \sigma T^{4}, \quad \sigma \approx 5.670 \times 10^{-8} \ \text{W m}^{-2} \text{K}^{-4}.
  • Small increases in temperature lead to large increases in total emission.
• Application to stars:
  • As a star heats up, its color shifts, its peak wavelength moves toward shorter wavelengths, and its brightness increases per Stefan–Boltzmann predictions.

The Electromagnetic Spectrum and Spectroscopy

• Spectroscopy is the study of spectra produced when light interacts with matter; it is a foundational tool for identifying elements and diagnosing physical conditions.
• Spectral types:
  • Continuous spectrum: produced by hot, dense sources (e.g., a filament or hot solid). The spectrum contains all wavelengths without interruption.
  • Emission spectrum: produced by hot, rarefied gas; shows discrete emission lines at specific wavelengths corresponding to atomic transitions.
  • Absorption spectrum: produced when a continuous spectrum passes through a cooler gas; atoms absorb photons at specific wavelengths, producing dark lines in the spectrum.
• Practical tool:
  • Spectra (emission and absorption lines) identify elements present in a source (e.g., Hydrogen, Sodium, Helium, Neon, Mercury) and reveal physical conditions.

Spectral Lines and Spectroscopes

• A spectroscope splits light into its component colors (spectrum) using refraction (prism) or diffraction.
• Spectral components:
  • Continuous spectrum (all colors) from hot, dense sources.
  • Emission lines: discrete colors emitted by atoms when electrons drop to lower energy levels.
  • Absorption lines: frequencies removed from a continuous spectrum by atoms absorbing photons.
• Practical displays:
  • Emission spectra of elements show bright lines at characteristic wavelengths (e.g., Hydrogen, Sodium, Helium, Neon, Mercury).
  • A visible spectrum from ~400 nm to ~700 nm is commonly observed in lab demonstrations.
• Example wavelengths (visible region):
  • Balmer/visible lines appear around wavelengths such as \lambda = 656.5\ \text{nm},\ 486.3\ \text{nm},\ 434.2\ \text{nm} corresponding to hydrogen transitions to n = 2 from n = 3, 4, 5 respectively (3→2, 4→2, 5→2).

Emission and Absorption Spectra: Element Identification

• Emission spectra can identify atoms because each element has a unique set of emission lines.
• Absorption spectra can also identify elements, as cool gas absorbs the same frequencies that its atoms emit when excited.
• Examples of observed elements in spectra include Hydrogen, Sodium, Helium, Neon, Mercury, Krypton, Argon.
• The spectra provide fingerprints for elements, enabling composition determination in stars, lamps, and laboratory plasmas.

Kirchhoff’s Laws of Spectroscopy

• Kirchhoff’s First Law (continuous spectrum):
  • Hot, dense gases or solids produce a continuous spectrum.
  • Example: light bulb filament.
• Kirchhoff’s Second Law (emission spectrum):
  • Hot, rarefied gas produces an emission spectrum consisting of bright lines at specific wavelengths.
  • Example: neon sign.
• Kirchhoff’s Third Law (absorption spectrum):
  • Cool gas in front of a hot, dense source produces an absorption spectrum with dark lines corresponding to the absorbed wavelengths.
  • Example: the Sun’s spectrum shows absorption lines from various elements.

Doppler Shift and Measurements of Motion

• Doppler shift concept:
  • Observed wavelengths shift depending on relative motion between source and observer.
  • Lines at rest wavelengths shift toward red (longer wavelengths) if the object is moving away; shift toward blue (shorter wavelengths) if moving toward us.
• Illustrative observations:
  • Object 1: lines redshifted → moving away from the observer.
  • Object 2: greater redshift → moving away faster than Object 1.
  • Object 3: blueshifted → moving toward the observer.
  • Object 4: greater blueshift → moving toward faster than Object 3.
• Simple non-relativistic Doppler relation (often used in introductory contexts):
  • \lambda{\text{observed}} = \lambda{\text{rest}} \left(1 + \frac{v}{c}\right) for small speeds v << c.

Atomic Structure and Radiation

• Atoms contain electrons in discrete energy levels and a nucleus made of protons and neutrons.
• The existence of spectral lines demanded a quantum model of the atom; the Bohr model introduced quantized energy levels to explain allowed and observed transitions.
• Electronic transitions:
  • An electron moves between energy levels by absorbing or emitting a photon with energy equal to the difference between the levels:
  • \Delta E = E{\text{upper}} - E{\text{lower}} = h\nu = \frac{hc}{\lambda}.
• Excited vs ground states:
  • An electron in a higher-energy shell than its ground state is in an excited state.
  • Excitation can occur via photon absorption or collisions with other particles.
  • An excited electron returns to a lower energy state by emitting a photon with energy equal to the energy gap, after which the system may return directly to ground state or cascade through intermediate levels.
• Decay pathways:
  • Direct decay: X → ground state emits a single photon.
  • Cascade: X → intermediate state → ground state, emitting photons at each step.
• Photons are quanta of electromagnetic radiation carrying specific energy, enabling discrete spectral features.
• Multielectron atoms produce more complex spectra than hydrogen due to many possible energy level configurations.

Hydrogen Atom and Balmer Series (Atomic Transitions)

• Emission energies correspond to differences between allowed levels; wavelengths appear as lines in the spectrum.
• Hydrogen Balmer series (transitions to n = 2):
  • 3→2: H-alpha line at approximately \lambda \approx 656.3\ \text{nm}
  • 4→2: H-beta line at approximately \lambda \approx 486.1\ \text{nm}
  • 5→2: H-gamma line at approximately \lambda \approx 434.0\ \text{nm}
• These lines illustrate how a single-electron system yields a set of discrete wavelengths.
• General hydrogen energy levels (Bohr model) can be summarized as:
  • E_n = - \frac{13.6\ \,\text{eV}}{n^2}, \quad n = 1,2,3,\dots
  • Radiative transitions occur when electrons move between these levels, with photons of energy equal to the difference of the levels.

The Electromagnetic Spectrum: Overview and Lab Context

• The electromagnetic spectrum spans from gamma rays to radio waves, with visible light lying in the ~400 to ~700 nm range.
• The lab context of spectroscopy includes observing spectra with a spectroscope, identifying elements from spectral lines, and linking spectral features to physical properties of sources.

Formation of Spectral Lines: Absorption and Emission in Atoms

• Absorption lines form when a photon causes an electron to jump from a low energy level to a higher one, removing that photon from the transmitted spectrum.
• Emission lines form when an electron in an excited state decays to a lower energy level, emitting a photon with energy equal to the energy gap.
• Decay pathways:
  • Direct decay to ground state (single photon).
  • Cascade through intermediate states (multiple photons at different wavelengths).
• Multielectron atoms yield more complex spectra due to more available energy levels and possible transitions.

Molecules: Spectra Beyond Atoms

• Molecules possess additional energy mechanisms:
  • Electronic transitions produce visible and ultraviolet lines (similar to atoms).
  • Vibrational transitions produce infrared lines (IR).
  • Rotational transitions produce radio-wave lines (microwave region).
• Molecular spectra are generally more complex than atomic spectra due to rotational-vibrational coupling and multiple possible transitions.
• Visual examples show molecular hydrogen spectra versus atomic hydrogen spectra to illustrate the greater complexity.

Visual Features: Energy Levels and Transitions (Name That Feature)

• Conceptual reminders used in the slides:
  • Ground state, first excited state, second excited state, etc., with transitions via UV photons or visible photons depending on the energy gaps.
  • Interpretation of spectra in terms of transitions between discrete energy levels.

Observational Notes: Wavelengths, Colors, and Measurement Scales

• Lab-scale spectra often display a range of wavelengths (e.g., 400–700 nm) with labeled emission lines corresponding to specific elements.
• A spectrum can be used to identify the element responsible for the lines when placed under a spectrum.
• The lab materials indicate a spectrum with lines labeled under the spectrum (Hydrogen, Sodium, Helium, Neon, Mercury, Krypton, Argon) across a visible range.

Practical Applications and Real-World Relevance

• What you can learn from a star’s spectrum:
  • Composition: which elements are present.
  • Direction of movement: via Doppler shifts of lines.
  • Speed: through redshift/blueshift magnitudes (radial velocity).
  • Temperature: inferred from the spectrum and peak emission using Wien’s law and color information.
• Spectral lines serve as fingerprints for elements used in laboratory plasmas, lamps, and astronomical observations.
• The interplay of emission, absorption, and continuous spectra informs us about physical conditions (density, temperature, optical depth) in celestial and laboratory environments.

Quick Lab Context and Upcoming Assessments

• Lab 4: Electromagnetic Spectrum / Spectroscopy
  • Involves observing spectra with a spectroscope, typically across the 400–700 nm visible range.
  • Elements present in the lab spectrum include Hydrogen, Sodium, Helium, Neon, Mercury, Krypton, Argon.
• Course Schedule:
  • Quiz due 8 pm Sunday (in the Quizzes folder) covering chapters 1–3.
  • Lecture Exam 1 scheduled for Thursday, Sept 11; bring a pencil and a Scantron; study guide and review quiz available on Blackboard.

Key Formulas and Numerical References (Summary)

• Wien’s displacement law:
  • \lambda_{\max} T = b
  • b \approx 2.898 \times 10^{-3}\ \text{m K}
• Stefan–Boltzmann law:
  • j^* = \sigma T^{4}
  • \sigma \approx 5.670 \times 10^{-8}\ \text{W m}^{-2}\ \text{K}^{-4}
• Photon energy and relation to wavelength:
  • E = h\nu = \frac{hc}{\lambda}
• Electron energy levels (hydrogen-like):
  • E_n = -\frac{13.6\ \text{eV}}{n^{2}}
• Hydrogen Balmer series wavelengths (visible lines):
  • \lambda{3\to 2} \approx 656.3\ \text{nm},\quad \lambda{4\to 2} \approx 486.1\ \text{nm},\quad \lambda_{5\to 2} \approx 434.0\ \text{nm}
• Doppler shift (non-relativistic approximation):
  • \lambda{\text{observed}} = \lambda{\text{rest}} \left(1 + \frac{v}{c}\right)

Connections to Foundational Principles

• Spectroscopy interlinks quantum mechanics (discrete energy levels) with thermodynamics (blackbody radiation) and relativity (Doppler shifts for moving sources).
• The concept of photons as energy quanta bridges particle and wave descriptions of light, explaining both emission/absorption lines and blackbody behavior.
• The Bohr model provides a simple framework for hydrogen-like spectra, while multi-electron atoms and molecules require more complex quantum mechanical treatments for accurate spectral predictions.