5. The Nature of Light
• Light travels in vacuum at 3.0 . 108 m/s
• Light is one form of electromagnetic radiation
• Continuous radiation: Based on temperature
• Wien’s Law & the Stefan-Boltzmann Law
• Light has both wave & particle properties
• Each element has unique spectral lines
• Atoms: A nucleus surrounded by electrons
• Spectral lines: Electrons change energy levels
• Spectral lines shift wavelength due to motion
Does Light Travel Infinitely Fast?
• Some ancient common experiences
– Lightning & thunder
• At minimum,
light travels faster than easily measured
• At maximum, light
might travel infinitely fast
– Galileo’s experiments
• Human reflexes are much too slow
• Human pulse
is much too long
• Olaus Rømer 1676
– Inconsistencies in occultations of Jupiter’s moons
• Earlier than expected with Jupiter closer than average
• Later than expected with Jupiter farther than average
EMR Travels At Finite Speed
Occultation
Occultation
Light Moves in Vacuum 3.0 . 108 m/s
• Light travels at constant speed in
vacuum
– Recognized by Einstein as highest possible speed
– Independent of the speed of any observer
– That speed is…c…and is…
“celeritas”
c = 3.0 . 105 km/s
c = 3.0 . 108 m/s
c = 3.0 . 1010 cm/s
• Light travels different speeds in different media
– Air
slows light a little
Low density
• Light bends/refracts a little as it enters the atmosphere
– Glass slows light a lot
High density
• Light bends/refracts a lot as it enters a telescope lens
“Light” is Electromagnetic Radiation
• “Light” is one form of electromagnetic radiation
– Electric & magnetic components are sine waves
• Electric & magnetic components identical wavelengths
• Electric & magnetic components perfectly synchronized
• Various regions electromagnetic radiation
–R
Radio
–I
Infrared
–V
Visible
–U
Ultraviolet
–X
X-ray
– G Gamma-ray
Longest λ’s
Low energies
“Light”
Medium energies
Shortest λ’s
High energies
EMR: Electric & Magnetic Waves
• Wave properties
– Electric
vector vibrates in a sine wave form
vibrates in a single plane
– Magnetic vector vibrates in a sine wave form
vibrates perpendicular to e– vector
vibrates synchronized w/e– vector
Refraction of Sunlight By a Prism
The “Celebrated Phenomenon of Colours”
Red light is
refracted least
Blue light is
refracted most
Prisms Do Not Add Color to Light
• Newton’s prism experiments
– Isolate one color from sunlight using one prism
– Pass
that color through a second prism
• No color is added
The Electromagnetic Spectrum
Emission & Absorption Spectra
• Emission
spectra
Bright = Hot
Looking directly at a hot high-density object
– Continuous  Hot
high-density objects
• Hot stars with no intervening interstellar gas clouds
– Bright-line
 Hot
low-density objects
• Hot interstellar gas clouds between any star & the Earth
• Absorption
spectra
Dark = Cold
Not looking directly at a hot high-density object
– Dark-line
 Cool low-density objects
• Cool interstellar gas clouds
Continuous and Line Spectra
Absorption from a cool
low density object
+
=
Emission from a hot
high density object
Emission from a hot
low density object
The Blackbody Concept
• Blackbody: An ideal concept
– Absorbs 100% of all wavelengths of incident EMR
• All X-rays, visible light, radio waves…
• Experience shows that this is impossible
– Emits all absorbed energy as blackbody radiation
• Radiation based exclusively on Kelvin temperature
• Experience shows that this actually happens
• Wien’s Law
– Wavelength at which the most energy is produced
• Stefan-Boltzmann Law
– Total energy is proportional to T4
Blackbody Curve: The Ideal
“White” stars
Our Sun
“Red” stars
Blackbody Curve: The Sun
Wien’s Law
• Blackbody radiation curves have one peak
– This wavelength
emits the most energy
– This wavelength depends on Kelvin temperature
0.0029
lmax =
T
lmax = Wavelength of maximum emission (meters)
T = Temperature
(kelvins)
•
lmax is inversely proportional to Kelvin temp.
– Higher temperature  Shorter wavelength
The Stefan-Boltzmann Law
• Blackbody radiation curves show energy flux
– This energy flux depends on Kelvin temperature
F = s ×T
4
F = Energy flux
(joules . m–2 . sec–1 )
s = Constant = 5.67 . 10–8 W . m–2 . K–4
TK = Temperature
(kelvins)
• Energy is directly proportional to TK4
– Raising TK by a factor of 10 raises energy by 10,000
The Wave-Particle Nature of EMR
• EMR behavior depends on the experiment
– Wave
experiment: EMR behaves like a wave
• Young’s double-slit experiment
– Particle experiment: EMR behaves like a particle
• EMR as photons
– A quantum amount of EMR energy
– Energy = Planck’s Constant . Frequency
• The photoelectric effect
– Electron emission requires some minimum energy
• Possible only if photons actually exist
Each Element Has a Unique Spectrum
• Every material has a unique spectral signature
– Unique set of spectral lines
• When hot, the spectral lines are bright
• When cool, the spectral lines are dark
– Each spectral line has a unique l
Spectroscopy
– Each spectral line emits a unique amount of energy
• Kirchhoff’s Laws
– Hot
opaque
objects:
Continuous spectra
• Classical blackbody radiation
– Hot transparent objects:
Bright-line
spectra
• Hot interstellar gas clouds with no continuous background
– Cool transparent objects:
Dark-line
spectra
• Cool interstellar gas clouds with a continuous background
The Periodic Table of the Elements
Spectra: The Hydrogen Family
Spectra: The Helium Family
Spectra: The Beryllium Family
Spectra: The Boron Family
Spectra: The Carbon Family
Spectra: The Nitrogen Family
Spectra: The Oxygen Family
Spectra: The Fluorine Family
The Bohr Model of the Atom
• A central nucleus
– One or more protons
Atomic number
• Determines the chemical properties (elements)
– Zero or more neutrons
• Determines the nuclear
Mass
number
properties (isotopes)
• Electron orbitals surround the nucleus
– Neutral atoms: Number of p+ = Number of e–
– Ionized atoms: Number of p+ ≠ Number of e–
• Cations: One or more e–
• Anions:
lost
One or more e– gained
Net positive charge
Net negative charge
Bohr Model of the Hydrogen Atom
Electron orbitals are not to scale
Hydrogen Electron Transitions
Electrons Jump Energy Levels
• Electrons jumping energy levels produce lines
– Hydrogen atom is the simplest of all
• Lyman
series:
Ultraviolet spectrum
• Balmer
series:
Visible
spectrum
Infrared
spectrum
• Paschen series:
– All other atoms & elements are more complicated
• More considerations about spectral lines
– Each line has a different
amount of energy
• Energy = Planck’s constant . Frequency
– Each line has a different probability of jumping
• More jumps  More energy emitted  Brighter lines
Spectra: Hydrogen Energy Levels
The Doppler Effect
• Effect
Wavelength shift due to relative motion
– Source & viewer moving closer
Blue shift
• Spectral lines shifted toward blue end of the spectrum
– The spectral lines do not actually appear blue ! ! !
– Source & viewer moving farther
Red shift
• Spectral lines shifted toward red end of the spectrum
– The spectral lines do not actually appear red ! ! !
• Cause
Relative motion of source & observer
– Source & viewer moving closer
• Waves compressed  Shorter wavelength  Blue shift
– Source & viewer moving farther
• Waves stretched  Longer wavelength  Red shift
Doppler Shift: Stretching Waves
Compressed wavelengths
Higher frequencies
Shift toward blue
Stretched wavelengths
Lower frequencies
Shift toward red
Important Concepts
•
Light in vacuum at constant speed
•
– 3.0 . 108 m . sec–2
•
Light in other media moves slower
– Wavelength of maximum energy
•
– Related generally to media density
•
Light is one form of EMR
–
–
–
–
–
–
•
Gamma rays
X-rays
Ultraviolet
Visible
Infrared
Microwave / Radio
•
Hot high density
Hot low density
Cool low density
Blackbody concept
– Absorbs 100% of all wavelengths
– Emits 100% at specific wavelengths
Stefan-Boltzmann Law
– Total energy produced
•
Wave-particle duality of all EMR
– Behavior depends on experiment
– Photoelectric effect
•
Unique sets of spectral lines
– Kirchhoff’s three laws
•
Bohr’s mode of hydrogen
– Nucleus with orbitals
– Neutral & ionized atoms
– Electron energy jumps produce lines
Emission & absorption spectra
– Continuous
– Bright line
– Dark line
Wien’s Law
•
Doppler effect
– Relative convergence: Blue shift
– Relative divergence: Red shift