Astronomy 114 - University Of Massachusetts Amherst

Astronomy 114Lecture 10: Quantum Mechanics & Doppler ShiftMartin D. Weinbergweinberg@astro.umass.eduUMass/Astronomy DepartmentA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—1/16

AnnouncementsProblem Set #2 solutions postedProblem Set #3 available now and due MondaySo I can post the solutions . . . sorry about thetiming.Concept “handout” onlineA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—2/16

AnnouncementsProblem Set #2 solutions postedProblem Set #3 available now and due MondaySo I can post the solutions . . . sorry about thetiming.Concept “handout” onlineToday:Blackbody radiationSpectraQuantum mechanicsLIGHT, Chap. 5A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—2/16

Types of SpectraA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—3/16

Kirchhoff’s Laws1. A dense (opaque) hot object emits a continuousspectrum2. A cool tenuous cloud emits discrete spectral lines3. A hot opaque object viewed through a cool cloudshows a continuous spectrum with absorption linesVirtually every astronomical observation fits in one ofthese categories!A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—4/16

Nature of matterAn atom consists of a small, dense nucleus surroundedby electrons (negative charge)Nucleus consists of protons (positive charge) andneutrons (no charge)Number of protons defines an elementAtoms with varying numbersof neutrons are calledisotopesAtoms with a varying numbersof electrons are called ionsA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—5/16

Quantum mechanics (1/2)Atoms, electrons, and nuclei no longer obeyNewton’s lawsWave-like properties of matter important for atomicparticles (or smaller)Consider hydrogen atom: 1 electron 1 protonAttractive force is is an inverse square, as ingravitationDrop the electron straight at the proton: series ofdistances where the electron will "hang" on its waydownWave nature of the electron that makes it "hang" atcertain distancesA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—6/16

Quantum mechanics (2/2)Examine the wave nature of the electron: its wavehas just one loop at the lowest possible energy level,2 loops at the next one up, . . .Must be a whole number of waves in the well or thecorresponding energy isn’t allowedEnergies of the electron in the atom are quantizedA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—7/16

Energy Levels (1/4)Bohr Model of the Hydrogen AtomElectron circles the nucleus (a proton) only in allowedorbits n 1, 2, 3, . . .In this model, n 2, 3, 4 energies arerespectively 4, 9, 16times larger thanthe n 1A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—8/16

Energy Levels (2/4)Hydrogen atom absorbs or emits a photon whose wavelength is 656.3 nm(a) The photon isabsorbed by theatom, causing theelectron to jumpfrom the n 2 orbitup to n 3A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—9/16

Energy Levels (2/4)Hydrogen atom absorbs or emits a photon whose wavelength is 656.3 nm(a) The photon isabsorbed by theatom, causing theelectron to jumpfrom the n 2 orbitup to n 3(b) The photon is emitted by the atom as the electronfalls from the n 3 orbit down to the n 2 orbitA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—9/16

Energy Levels (2/4)Hydrogen atom absorbs or emits a photon whose wavelength is 656.3 nm(a) The photon isabsorbed by theatom, causing theelectron to jumpfrom the n 2 orbitup to n 3(b) The photon is emitted by the atom as the electronfalls from the n 3 orbit down to the n 2 orbitQuantum jumpA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—9/16

Energy Levels (3/4)A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—10/16

Energy Levels (3/4)E hν hc/λA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—10/16

Energy Levels (4/4)Balmer figured out the pattern mathematically:111 R 2λ4 n where n 2 and R 1.087 107 m 1 (Rydbergconstant)A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—11/16

Energy Levels (4/4)Balmer figured out the pattern mathematically:111 R 2λ4 n where n 2 and R 1.087 107 m 1 (Rydbergconstant)General formula (Bohr, Schroedinger):111 R 22λMn where M is the index of the inner orbit and n is theindex of the outer orbit.A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—11/16

Explains the 3 types of spectra1. Continuous spectrum: intensity changes smoothly withwavelength; all colors represented; typical emissionfor hot, dense body2. Emission line spectrum: intensity at a few discretewavelengths only; called “line” because ofappearance using grating; typical of hot tenuous gas3. Absorption line spectrum: intensity smooth withwavelength except at few discrete wavelengths; dark“lines” caused by light from a hot body absorbed bylow energy atoms and moleculesA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—12/16

Doppler Effect (1/4)The wavelength of light is affected by motion between thelight source and an observerThe light source shown here is moving toward the leftCircles 1–4 indicate the crests oflight waves thatwere emitted bythe source whenit was at pointsS1–S4A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—13/16

Doppler Effect (2/4)The waves are crowdedtogether in front of themoving source but arespread out behind itConsequently, wavelengths appear shortened(blueshifted) if the source is moving toward theobserverThey appear lengthened (redshifted) if the source ismoving away from the observerA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—14/16

Doppler Effect (3/4)The change in wavelength is proportional to the velocity: λvr λλ1 λ2 vr cλλcλwhere vr is the radial velocityPositive velocity recedingNegative velocity approachingA114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—15/16

Doppler Effect (4/4)Doppler Formula: λcvr λExample:In a star, the Balmer line H-alpha is observed atλ 656.5 nm. What is the star’s radial velocity? (H-alpharest λ 656.3 nm.)Star is receding from us:0.2 nmvr 3 105 km/s656.3 nmSo vr 91 km/s.A114: Lecture 10—23 Feb 2007Read: Ch. 5Astronomy 114—16/16

Astronomy 114 Lecture 10: Quantum Mechanics & Doppler Shift Martin D. Weinberg weinberg@astro.umass.edu UMass/Astronomy Department A114: Lecture 10—23 Feb 2007 Read: Ch. 5 Astronomy 114—1/16