Week 3: Light HW2 due on Thursday Read Ch. 5 (can skip 5.5) Galillama Galilei ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 1
Let there be LIGHT! • Review of atomic structure, energy exchange processes, and spectroscopy • Radiative transfer • Thermodynamic equilibrium • Blackbody radiation • Wien’s Law ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 2
<latexit sha1_base64="G3XS+610iSabTSlMwBZ+vdiA+v4=">ACFHicbVDLSgMxFM3UV1tfoy7dBIsgiGVSwcdCKLoRVxXsA9taMmnahmYeJBmxDOM/uBH8CpduXCji1oU7v0YznS609UDgcM653Nxj+5xJZVlfRmpqemZ2Lp3Jzi8sLi2bK6sV6QWC0DLxuCdqNpaUM5eWFVOc1nxBsWNzWrX7J7FfvaZCMs+9UAOfNh3cdVmHEay01DK30W3YEA6klQgeQZTfswqwoZhDJUTWVbiDqMkcBZlW2bOyltDwEmCRiRXzPgPl4836W+dloeyRwqKsIx1LWkeWrZoiFYoTKNsIJPUx6eMurWvqYr2GQ6PiuCmVtqw4wn9XAWH6u+JEDtSDhxbJx2senLci8X/vHqgOgfNkLl+oKhLkWdgEPlwbgh2GaCEsUHmAimP4rJD0sMFG6x7gENH7yJKkU8mg3XzjXbRyDBGmwDjbAFkBgHxTBKSiBMiDgDjyBF/Bq3BvPxpvxnkRTxmhmDfyB8fEDQmWfjQ=</latexit> <latexit sha1_base64="9IZFE3rhkrO3cmwkp71S1czp4Nw=">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</latexit> “Light” is electromagnetic radiation of any wavelength/frequency, not just what eyes see Classically, can be thought of a wave traveling down an electric field line like an induced transverse wave down a rope. In QM, quanta of the wave are called photons, which have energy and momenta determined by wavelength/frequency. E = h ν = hc λ h = 6 . 626 × 10 − 34 J s = 4 . 135 × 10 − 15 eV s c = 2 . 998 × 10 8 m s − 1 ~ = h 1 eV = 1 . 602 × 10 − 19 J 2 π ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 3
ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 4
<latexit sha1_base64="PL9ef2vqR2zk4gaycuqGdusJ+Kk=">ACFnicbVDLTgIxFO3gC/GFunTiCZuxBlIlCXRjUtM5JEwOmUAo1tp2k7BEL4Cjd+iYkbFxLj1rjzQ3RtARcKnuQmJ+fcm3vCSWj2rjuh5NYWFxaXkmuptbWNza30ts7FR3FCpMyjlikaiHShFByoYaRmpSEcRDRqrh7cXYr3aJ0jQS16YvSYOjtqAtipGxUpA+vun5foHBEIfSamiHuSBhCfQK+RPJ46wjqYcjvUgnXGz7gRwng/JFM8+HwYde+SkH63W9GOZEGMyQ1nXPlaYxQMpQzMgw5ceaSIRvUZvULRWIE90YTN4awkOrNGErUraEgRP198QAca37PLSdHJmOnvXG4n9ePTatQmNAhYwNEXi6qBUzaCI4zg2qSLYsL4lCtqb4W4gxTCxiaZsiF4sy/Pk0ou6+WzuSubxjmYIgn2wD4Ah4A0VwCUqgDC4A4/gGYyce+fJeXFep60J52dmF/yB8/YNhqgrw=</latexit> <latexit sha1_base64="0a5L/kyuRDmRL+ob9UlvI6Jsq84=">ACDXicbVC7SgNBFJ31GRMfq5Y2g4lgY9hNwNgIQRvLCOYB2RhmJ5NkyMzsMjMbCEv8ABt/xUZBERsLezs/RGsnj0ITD1w4nHMv97jh4wq7Tif1sLi0vLKamItmVrf2Nyt3cqKogkJmUcsEDWfKQIo4KUNdWM1EJEPcZqfq985Ff7ROpaCu9CAkDY46grYpRtpITvDmyE8hW72uJCHnqacKOg61/FRrjC8iT3JYa8zbNpJ+uMAeJOyXpYubr8a2f+i417Q+vFeCIE6ExQ0rVXSfUjRhJTEjw6QXKRIi3EMdUjdUILO2EY+/GcIDo7RgO5CmhIZj9fdEjLhSA+6bTo50V816I/E/rx7p9kjpiKMNBF4sqgdMagDOIoGtqgkWLOBIQhLam6FuIskwtoEmDQhuLMvz5NKLuvms7lLk8YZmCAB9sA+OAQuKIAiuAlUAY3IJ78ASerTvrwXqxXietC9Z0Zhf8gfX+A3yMncI=</latexit> Atomic Structure (quantized energy levels) m p = 1 . 673 × 10 − 27 kg m e ≈ m p / 1836 m n ∼ m p ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 5
<latexit sha1_base64="27Lgzva+BgNAE1P3MWVuQo29Pi8=">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</latexit> Atomic Structure (quantized energy levels) Photon emitted with wavelength/ frequency equal to difference in energy between allowed orbits (energy levels) E n = − m e c 2 ↵ 2 Z n 2 2 e 2 1 1 ~ c ≈ 7 . 30 × 10 − 3 ≈ ↵ ≡ 4 ⇡✏ 0 137 ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 6
<latexit sha1_base64="bqw9mgF8fHl5v7Lg+vyS8IO63Cw=">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</latexit> Energy Levels ∆ E = E n − E n 0 = � ( n 0 ) 2 − 1 1 (13 . 6 eV) Z 2 n 2 (Energies correspond to neutral hydrogen) ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 7
Absorption of Energy Photoexcitation Collisional Excitation ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 8
Absorption of Energy Photoionization Collisional Ionization ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 9
Emission of Energy Stimulated Emission Spontaneous Emission Collisional De-excitation ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 10
Emission of Energy Radiative Recombination ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 11
Kirchoff’s Laws • A solid, liquid, or dense gas produces a continuous spectrum. • A tenuous gas in front of a hot background produces an absorption spectrum. • A tenuous gas in front of a cool background produces an emission spectrum. ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 12
ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 13
ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 14
<latexit sha1_base64="bqw9mgF8fHl5v7Lg+vyS8IO63Cw=">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</latexit> Spectra are like Fingerprints They encode what and how much of an element is present in a gas (of a cloud, star, etc.), how hot it is, and whether it’s being excited by something else Each element has a unique pattern of lines, which can be seen in absorption or emission ∆ E = E n − E n 0 = � ( n 0 ) 2 − 1 1 (13 . 6 eV) Z 2 n 2 ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 15
Stellar Types (different masses/temperatures) ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 16
<latexit sha1_base64="STxWXR7tpGVxIUjG4Vm4zWTgYDw=">ACJHicbVBNS8MwGE7n15xfVQ8iXoJD8DTaeXAgwlAPHie4D1jLSN0C0vTkqTCLPsxXvwrXjxMxYMe9OrPMPsQdPOFhIfng+R9vJhRqSzrzcjMzS8sLmWXcyura+sb5uZWTUaJwKSKIxaJhockYZSTqKkUYsCAo9Rupe93yo12+IkDTi16oXEzdEbU4DipHSVMs8uYWn0AkEwqlzQZhC0GE67aN+gNmDzRor5aZt4qWKOBs8CegHy59DnYef/arbTMZ8ePcBISrjBDUjZtK1ZuioSimJF+zkiRHuojZpashRSKSbjpbswPN+DCIhD5cwRH7O5GiUMpe6GlniFRHTmtD8j+tmaig5KaUx4kiHI8fChIGVQSHjUGfCoIV62mAsKD6rxB3kC5E6V5zugR7euVZUCsW7KNC8Uq3cQbGkwV7YB8cAhscgzK4BVQBRjcgQcwAE/GvfFovBivY2vGmGS2wZ8xPr4BaiCpGg=</latexit> unshifted Doppler Shift “blueshifted” z = ∆ λ = ∆ ν λ ν “redshifted” unshifted Allows us to infer motions along the “line of sight” ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 17
Lines are not delta functions! i.e., the difference b/t energy levels is NOT exact Motion-induced Broadening (small Doppler shifts cause Other Types of Broadening lines to appear more broad) • Thermal Broadening • Natural Broadening • Rotational Broadening • Pressure Broadening • Turbulent Broadening • Zeeman Broadening broadened ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 18
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