1445 Introductory Astronomy I

1. 1445 Introductory Astronomy I Chapter 4 Thermal Radiation and Atomic Spectra R. S. Rubins Fall, 2010

2. Thermal Radiation 1 • Every object in the universe emits EM radiation, and also absorbs EM radiation from its surroundings. • A blackbody (or thermal radiator)is an idealized object which absorbs all the EM radiation falling on it. • The radiation emitted by a blackbody depends only its temperature. • Thus, the temperature of a distant blackbody can be determined simply from the radiation it emits. • This result enables us to determine the surface temperatures of distant stars, and even more distant galaxies just by carefully measuring the radiation they emit.

3. An Ideal BlackbodyAn ideal blackbody is a cavity with a small aperture.

4. Thermal Radiation: Intensity Curves 1 The intensity-wavelength curve at one temperature lies above that for a lower temperature at all wavelengths. Objects (which do not vaporize or burn) become red hot at about 2000 K, white hot at about 5000 K, and blue hot above 8000 K.

5. Spectral Types 1

6. Spectral Types 2

7. 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 supervised a graduate student, Ernest Marsden, suggesting he look for α-particles scattered backwards, when fired at a gold target. • The surprise result obtained by Marsden conflicted with the prevailing plum pudding model of the atom, and lead Rutherford to propose the nuclear atom. • Comparison of the experimental results with the Rutherford’s theoretical calculations, enabled him to determine the diameter of an atomic nucleus, which is 10–15to 10–14 m.

8. Nuclear Atom 1

9. Nuclear Atom 2 9

10. Nuclear Atom 2

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

12. Bohr Model 2 • Radius of the n’th allowed orbit rn = n2 r1, where the lowest orbit has n = 1 and r1 = 0.05 nm. The letter n represents the principal quantum number, which may only have the integer values 1, 2, 3, etc. For example, the radius of the n=3 orbit 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.

13. Bohr Model 3

14. Bohr Model 4 Photon absorption Photon emission 14

15. Bohr Model 5 In both cases, the photon energy is hc/ = E3 – E2.

16. Bohr Model 6

17. Obtaining a Line Spectrum An emission line spectrum A prism is shown above, but in practice, a diffraction grating would be used.

18. Absorption Line-Spectrum of H

19. Bohr Theory and H Spectra The visible Balmeremission lines are caused by transitions which end at the n=2 level.

20. Elemental Line Spectra

21. 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.

22. Doppler Effect 1 • The Doppler effect is the change of wavelength λ(and frequency f) which occurs when the source of waves and the observer are in relative motion. • λ and f for 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, f increases and; this is known as ablueshift. • When the source and observer separate from each other, f decreases and λincreases; this is known as a redshift.

23. Doppler Effect 2

24. Doppler Calculation of Velocity Ifλis the wavelength of a spectral line observed from a star with a radialvelocityv, and λois 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, so that v/c is negative. A receding source gives a redshift, since λ>λo, so that v/c is positive. ExampleIf a spectral line measured in the lab as 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 c, with the minus sign indicating that the star is movingtowards the Earth; i.e. a blueshift.