Atomic Spectra & Doppler Shift

Demos for Optics from last time

• Optical Board– Lens & mirror– Kepler & Galileo Telescope (inverts/does not)– Eye: normal, near, far sighted– Prism: different color (red/green) different

angle

iSkylab Stage 2

• How to estimate the period of the “second” motion (seasonal or montly)– Sun: we are measuring the decrease of altitude

per day. Expect: 4 x 23.5 deg = 97 deg• Example: you measured 0.5 deg/ day = 365*0.5

deg/year

– Moon: either same as sun, or, if you measured motion with respect to stars, e.g. 10 deg/ day = 300 deg/month

Measuring Temperatures

• Find maximal intensity

Temperature (Wien’s law)

Identify spectral lines of ionized elements Temperature

Color of a radiating blackbody as a function of temperature

• Think of heating an iron bar in the fire: red glowing to white to bluish glowing

Spectral Lines – Fingerprints of the Elements

• Can use this to identify elements on distant objects!

• Different elements yield different emission spectra

Kirchhoff’s Laws: Dark Lines

Cool gas absorbs light at specific frequencies

“the negative fingerprints of the elements”

Kirchhoff’s Laws: Bright lines

Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”

Kirchhoff’s Laws

1. A luminous solid or liquid (or a sufficiently dense gas) emits light of all wavelengths: the black body spectrum

2. Light of a low density hot gas consists of a series of discrete bright emission lines: the positive “fingerprints” of its chemical elements!

3. A cool, thin gas absorbs certain wavelengths from a continuous spectrum dark absorption ( “Fraunhofer”) lines in continuous spectrum: negative “fingerprints” of its chemical elements, precisely at the same wavelengths as emission lines.

Spectral Lines • Origin of discrete spectral lines: atomic structure of matter

• Atoms are made up of electrons and nuclei– Nuclei themselves are made up

of protons and neutrons

• Electrons orbit the nuclei, as planets orbit the sun

• Only certain orbits allowed Quantum jumps!

• The energy of the electron depends on orbit• When an electron jumps from one orbital to

another, it emits (emission line) or absorbs (absorption line) a photon of a certain energy

• The frequency of emitted or absorbed photon is related to its energy

E = h f

(h is called Planck’s constant, f is frequency)

Demonstration

• Gas Lamps

• Which one is He, which is H?

• Combined, you are looking at 99% of the (non-dark) matter content of the universe!

Energy & Power Units

• Energy has units Joule (J)

• Rate of energy expended per unit time is called power, and has units Watt (W)

• Example: a 100 W = 100 J/s light bulb emits 100 J of energy every second

• Nutritional Value: energy your body gets out of food, measured in Calories = 1000 cal = 4200 J

• Luminosity is the same as power radiated

Stefan’s Law

• A point on the Blackbody curve tells us how much energy is radiated per frequency interval

• Question: How much energy is radiated in total, i.e. how much energy does the body lose per unit time interval?

• Stefan(-Boltzmann)’s law: total energy radiated by a body at temperature T per second: P = A σ T4

• σ = 5.67 x 10-8W/(m2 K4)

Example: Stefan-Boltzmann Law

• Sun T=6000K, Earth t=300K (or you!)

• How much more energy does the Sun radiate per time per unit area?

• Stefan: Power radiated is proportional to the temperature (in Kelvin!) to the fourth power

• Scales like the fourth power!

• Factor f=T/t=20, so f4 =204=24x104=16x104

160,000 x

Example: Wien’s Law• Sun T=6000K, Earth t=300K (or you!)

• The Sun is brightest in the visible wave lengths (500nm). At which wave lengths is the Earth (or you) brightest?

• Wien: peak wave length is proportional to temperature itself Scales linearly!

• Factor f=T/t=20, so f1 =201=20, so peak wavelength is 20x500nm=10,000 nm = 10 um

• Infrared radiation!

Homework Questions

• Boltzmann: Scaling: area = R^2, T^4

Activity: Black Body Radiation

• Pick up a worksheet• Form a group of 3-4 people• Work on the questions on the sheet• Fill out the sheet and put your name on top• Hold on to the sheet until we’ve talked about

the correct answers• Hand them in at the end of the lecture or during

the break• I’ll come around to help out !

Doppler Shift

• From Wikipedia

Doppler Shift

• Can use the Doppler shift to determine radial velocity of

distant objects relative to us

• Transverse velocity can be measured from the motion of stars with respect to back-ground over a period of years– (Halley 1718: Sirius, Arcturus, Aldebaran

moved since Hipparchus, 1850 years ago)

Not Used

Homework: Doppler Shift of Hydrogen spectrum

• The discrepancy between the wavelength of a line measured in the lab versus measured on an object is proportional to the velocity of the object

• Apparent/ true wavelength = 1+ velocity/c

• Example: – Observed(or apparent): 698 nm

– Actual(or true or lab) wavelength: 656.3nm

– velocity = (698nm/656.3nm -1) c = 19100 km/s

Group Activity: Estimate Power

• Estimate how much energy you radiate per second

• Estimate how many candy bars you would have to eat per day to be able to do that

• Ponder the paradox

Doppler Shift and Stellar Magnitudes