Doppler Shift

1. Doppler Shift Defined as the shift in observed wavelength (dependent on the relative motion of the source and the observer)

2. Doppler shift cont’d. Red Shift Blue Shift When an object is approaching, the light waves appear to be getting shorter. • When an object is receding, the light waves appear to be getting longer, or moving towards the red end of the spectrum

3. Formula z times the speed of light gives the speed at which the star is receding

4. Redshift • The bottom represents a ‘stationary star’’s spectra (characterizing it’s elements). The subsequent images represents galaxies in motion (of similar composition). Because the emission lines have shifted further towards the red, the galaxies are moving away.

5. Bright Line and Absorption Spectra

6. Atoms can absorb energy (in the form of EM radiation) • Electrons exist at specific ‘distances’ from the nucleus. • Each allowed distance is an energy level • If left undisturbed, atoms like to bind electrons as tightly as possible, so electrons are generally found in lowest energy levels • If the atom is immersed in a beam of light, sooner or later the atom will encounter a photon with an energy of just the right amount to jump the electron up to the next higher energy level. The photon is absorbed, and "gone" from the beam of light coming from the star! Since the absorbed photon had a specific energy, this absorption occurs at a specific wavelength in the spectrum. • Atom is in an "excited" state • Ex) Like a kid right before Halloween, electron has higher energy. Eventually, electron (and child) drop back to the lower energy level • Atom must lose energy to drop, so it releases a photon of the same energy as the one it absorbed • Called emission • Atom could have absorbed another photon with the energy needed to jump up another energy level • If a photon with sufficiently large energy gets absorbed, it can cause an electron to become unbound from its nucleus (ionization). • Pattern of absorptions (or emissions) is unique to each element causing a recognizable pattern of absorption/emission lines in a spectrum.

7. Hydrogen

8. Light Intensity

9. Definition • The intensity of a beam of light is related to the number of photons. • Higher frequency means greater energy. • More photons equal greater intensity.

10. Inverse square law • i=1/r^2 • Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. • The intensity of the influence at any given radius r is the source strength divided by the area of the sphere.

11. SI Units • Candela • Defined to be the intensity of a light source producing single-frequency light at a frequency of 540 terahertz (THz) with a power of 18.3988 milliwatts over a complete sphere centered at the light source. • To produce 1 candela of single-frequency light of wavelength l, a lamp would have to radiate 1/(683V(l)) watts per steradian, • where V(l) is the relative sensitivity of the eye at wavelength l.

12. Energy and momentum of photons • photons are usually symbolized by hν, the energy of a photon, where hisPlanck's constant and the  ν is the photon's frequency • energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p