Astronomy 103: 5-Astronomical Spectra and Thermal Radiation
Topics Covered Today
Light and Atoms: Emission and absorption spectra
Astronomical Spectra: Understanding light properties in astronomy
Thermal Radiation:
Thermal radiation spectrum
Measuring temperature and energy flux of stars
Properties of Light
Light can be described as both a wave and a particle (Quantum Mechanics).
A light wave is characterized by:
Wavelength (BB): Distance between wave crests.
Frequency (f): Number of wave crests per second.
Speed of Light (c): Constant value
c = BB f = 3.00 imes 10^8 ext{ m/s}
Individual packets of light are called photons.
Photon energy (E) is given by:
E = hf = rac{hc}{BB}
(Where h is Planck’s constant)
Spectral Measurements
Spectrum Definition: A graph depicting intensity of light as a function of wavelength.
Units of Wavelength: Usually measured in nanometers (nm).
Wavelength Range (nm):
400 (violet) to 700 (red).
The Nature of Matter
An atom's nucleus consists of protons and neutrons.
Electron Orbitals: Regions surrounding the nucleus where electrons exist with specific energy levels.
Electrons can transition between orbitals by gaining or losing energy.
Review Question
The light emitted or absorbed by an atom in electronic transitions can be characterized by one number, which is:
A. Wavelength
B. Frequency
C. Energy
D. Any of the above
Atomic Interactions in Gases
When atoms are gathered in a gaseous state:
They exhibit random motion and collision, yet mostly consist of empty space with a large electron cloud.
Collisions primarily involve electrons, allowing energy exchange via photon emission or absorption.
Diffuse Gas Behavior: Low-density atoms have minimal interaction; emission and absorption still occur at discrete wavelengths related to the atom's energy levels,
Identifying Composition with Emission Spectra
By recording an emission spectrum, one can determine the gas cloud’s composition:
Common gases include: Hydrogen, Sodium, Helium, Neon, Mercury.
Photon Energy Interactive Scenario
Question Scenario: A photon with energy 1.92 eV interacts with hydrogen where two electron orbitals have an energy difference of 1.89 eV.
Possible responses:
A. Photon is not absorbed (not enough energy).
B. Photon is absorbed (sufficient energy for electron transition).
C. Photon is not absorbed (incorrect interpretation of photon nature).
Spectral Emission Characteristics
A diffuse gas emits an emission line spectrum; however, a dense gas or solid emits continuous thermal radiation.
Dense Objects Interaction: Photons are absorbed and re-emitted multiple times before escaping, complicating photon interactions with fixed energy levels.
Continuous thermal emission results from dense (opaque) gases or solids.
Temperature and Thermal Radiation
Temperature Definition: A measure of atomic energy and motion.
Low-temperature objects have less atomic movement.
High-temperature objects exhibit fast-moving atoms and energetic collisions.
Temperature Scales: Three primary scales:
Fahrenheit, Celsius, Kelvin.
Most common in physics and astronomy: Kelvin (0 K = absolute zero).
Conversion formula:
Typical stellar temperatures range from 2000 K to 20,000 K.
Collisional Energy and Photon Emission
As temperatures increase, substances collide more violently, emitting photons with an energy proportional to collision intensity.
Long-wavelength radiation: Produced from gentle collisions.
Short-wavelength radiation: Produced from hard collisions.
Characteristic spectrum of thermal radiation correlates with the number of photons emitted.
Planck's Law and Thermal Radiation Spectrum
The thermal radiation spectrum's shape varies with temperature:
As temperature rises:
Increased number of energetic collisions shifts the peak to shorter wavelengths (blue shift).
Overall brightness increases.
Thermal radiation properties are temperature-dependent, not material-specific.
Laws Governing Thermal Radiation
Wien’s Law
Observation: Hotter bodies emit more strongly at shorter wavelengths.
Peak Wavelength Relation:
BB_{max} ext{ is inversely proportional to temperature}
Stefan-Boltzmann Law
Total Energy Flux Relation:
F = C3 T^4
Where:
F = Energy flux (Watts/m²)
C3 = Stefan-Boltzmann constant C3 = 5.7 imes 10^{-8} ext{ Watts/(m² K^4)}
T = Temperature in Kelvins.
The Sun has an energy output of about 64 million watts per square meter.
Measuring Stellar Luminosity
Luminosity is the total energy output per second and can be calculated through:
ext{Luminosity} = C3 T^4 imes ext{Star's Surface Area} = C3 T^4 imes 4C0 R^2
Where R is the radius of the star.
Types of Spectra
Continuous Spectrum: Produced by hot, dense gases. Example: Incandescent light bulb spectrum.
Emission Line Spectrum: Produced by hot, diffuse gases; emits discrete wavelengths that depend on composition and temperature.
Absorption Line Spectrum: Occurs when cool diffuse gas absorbs specific wavelengths against a continuous spectrum, leaving dark lines (absorption lines).
Solar Spectrum and Spectrographs
The solar spectrum showcases both continuous and absorption characteristics viewed through a high-resolution spectrograph.
Dark bands indicate absorption lines from specific element transitions.
Review Questions
What kind of spectrum is the solar spectrum?
A. Emission spectrum
B. Continuous spectrum
C. Absorption spectrum
D. None of the above
Upcoming Engagements
Astronomy Discussion Exercise:
Aim: Review math skills relevant for the semester (graded for completion).
Public Observation Nights at Washburn Observatory:
Frequency: Every other Wednesday (next on March 18).
Timing: From 7:00 PM, changing to 9:00 PM after April 1.
Confirmation against weather conditions is encouraged.
Conclusion
Identifying elemental composition and temperature through spectral analysis is a crucial aspect of contemporary astronomy. Understanding thermal radiation laws, spectra types, and their applications are fundamental to evaluating celestial objects.