1446 Introductory Astronomy II

1. 1446 Introductory Astronomy II Chapter 4 Radiation, Spectra & the Doppler Effect R. S. Rubins Fall 2011 1

2. Thermal Radiation 1 • Every object in the universe emits EM radiation, and also absorbs EM radiation from its surroundings. • A blackbodyis an object which absorbs all the EM radiation falling on it. • An ideal blackbody is a cavity with a small aperture. • A black material, such as soot, is a perfect absorber in the visible region, but necessarily at other wavelengths. • An object at a constant temperature, emits the same amount of energy as it absorbs. • Thus, a good absorber is a good emitter, and vice versa. • An object absorbing more energy than it emits becomes hotter, one emitting more energy, becomes cooler. 2

3. Thermal Radiation 2 • An ideal emitter emits thermal(or blackbody) radiation in a combination of wavelengths that depending only on its temperature. • Thus, the temperature of a distant thermal emitter can be determined simply from the radiation it emits. • Since stars are almost perfect thermal radiators, their temperatures may be obtained from Earth-based measurements. An ideal blackbody (or thermal emitter) is a cavity with a small aperture. 3

4. Thermal Radiation from Stars UV IR visible Peak in IR Peak in visible Peak in UV 4

5. Thermal Radiation 3 • Solids or liquids become red hot at about 2000 K, white hot at about 5000 K and blue hot above 8000 K. 12,000 K, peak in UV 6000 K, peak in visible 3000 K, peak in IR 5

6. Color Sensitivity of the Eye blue red 6

7. Sunlight: Thermal Radiation at 5800 K 7

8. Thermal Radiation 4 Three results for thermal (or blackbody) radiation • As an object gets hotter, it emits more energy per second (or power) at all wavelengths; • Wien’s Law As the temperature increases, the peak of the intensity vs. wavelength curve moves to shorter wavelengths; i.e. λmaxT = constant or λ2/λ1 = T1/T2 . • Stefan-Boltzmann Law The total EM energy emitted per second (or power) is proportional to the fourth power of the temperature; i.e. P = constant x T4 or P2/P1 = (T2/T1)4. 8

9. Spectral Types 1 9

10. Spectral Types 2 10

11. Spectral Types 3 11

12. Spectral Types 4 12

13. Absorption and Emission Spectra Upper spectrum: absorption lines from the Sun. Lower spectrum: emission lines of vaporized iron. 13

14. Visible Spectrum from the Sun

15. Absorption Line-Spectrum of Atomic Hydrogen 15

16. Ernest Rutherford • He was born on a farm in New Zealand in 1871. • He shared the 1908 Nobel Prize in Chemistry for finding that one radioactive element can decay into another. • In 1907, at Manchester University, England, he suggested that his graduate student, Ernest Marsden, look for α-particles scattered backwards, when fired at a gold target. • Gold was chosen for this experiment, because it can be rolled very fine, and has a relatively massive nucleus. • He was astonished when Marsden obtained a positive result. • This result was in conflict with J. J. Thomson’s plum pudding model of the atom -– leading Rutherford to propose the nuclear atom in 1911. 16

17. Nuclear Atom 1 17

18. Nuclear Atom 3 H atom 18

19. Nuclear Atom 2 19

20. Bohr Model 1The negative electron orbits the positive nucleus. 20

21. Bohr Model 2 • Radius of the n’th allowed orbit rn = n2 r1, where the lowest (or ground) state has n = 1 and r1 = 0.05 nm. n (= 1, 2, 3, etc.) is the principal quantum number. • e.g. the radius of the 3rd lowest state (n=3) is r3 = 9r1 = 0.45 nm. Non-radiative orbits • According to Bohr’s hypothesis, the electron orbits the nucleus without radiating EM energy. • This result conflicts with classical EM theory, which requires an accelerating charge to radiate EM energy. 21

22. Bohr Model 3 Photon absorption Photon emission 22

23. Bohr Model 4 23

24. Bohr Model 5 24

25. Bohr Model 6 25

26. Successes of the Bohr Theory • It was the first model to give an explanation of narrow line-spectra. • The radius of the n =1 orbit (52.9 nm) was calculated to be in quantitative agreement with that of the H atom measured by X-ray crystallography. • The energy needed to eject an electron from an H atom from the n=1 orbit (13.6 eV) was in quantitative agreement with chemical measurements of the binding energy of H. • The values obtained for the wavelengths of the Balmer spectrum of H were in quantitative agreement with the wavelengths obtained experimentally (see next slide).

27. Bohr Theory and H Spectra • The Balmer emission lines are transitions to the n=2 level. 27

28. Failures of the Bohr Theory • There appeared to be no logical reason for the values of the of the allowed radius; however, one was obtained by Louis de Broglie in 1923, using a “standing” wave picture. • Bohr assumed that an electron in a stable orbit would not radiate energy, which was in direct contradiction with a basic rule of EM theory, that an accelerating charge must radiate EM energy, which would cause the electron to collapse into the nucleus. • Bohr’s Theory could was limited to the H atom, since every other atom of the periodic table contained more than one atomic electron, and he could not extend the theory to take the repulsion between electrons of larger atoms into account .

29. Representation of a Many-Electron Atom 29

30. Electronic Charge “Clouds” • Improved representations of electronic orbits for “excited” n=2 states of an H atom. • The quantum mechanical solutions represent the probability distributions (or charge clouds). • The darker the shade of blue, the higher is the probability of finding the electron in that region. 30

31. Doppler Effect 1 • The Doppler effectis the change of wavelength (and frequency) which occurs when the source of waves and the observorare in relative motion. • Wavelength λand frequency f of a wave moving with speed v are related by the equation v = f λ, so that higher frequency means shorter wavelength, and vice-versa. • When the source and observer approach each other, the frequencyincreases and the wavelengthshortens; this is known as a blueshift. • When the source and observer move apart, the frequencydecreases and the wavelength lengthens; this is known as a redshift. • Note: only for visible wavelengths are the actual shifts towards the blue or the red. 31

32. Doppler Effect 2 32

33. Radial and Transverse Doppler Effects 33

34. Barnard’s Star: Transverse (Proper) Motion Transverse motion of Barnard’s star 34

35. Calculating the Radial Velocity • If λ is the wavelength of a spectral line observed from a star with a radialvelocityv, λo is the wavelength of the that spectral line observed in the lab, then, if v << c, (λ–λo)/ λo= v/c. • An approaching source gives a blueshift, since λ<λo,sothat v/c is negative. • A receding source gives a redshift, sinceλ>λo, so that v/c is positive. • Example If a spectral line measured in the lab at 400 nm, appears at 396 nm when measured from a star, the star’s velocity is given by v/c = (396 – 400)/400 = – 4/400 = – 0.01. Thus, v = – 0.01 ctowards the Earth (blueshift). 35