1. 07.07.2011Lect. 5, gratings&light, 07.07.20111 CAPSTONE Lecture 5: Radiation from atoms

2. 07.07.2011Lect. 5, gratings&light, 07.07.20112 Radiation, Gratings Light brings most of our knowledge about stars. Waves have the property that they can be made to interfere. Popsicle sticks in pools, boat wakes crossing, etc. Light striking a grating leads to interference behind (transmission) or in front (refection) of the grating. The more grooves, the higher the dispersion. nm =sin  1 + sin  2 : n=no. of grooves per mm; m= order number; lambda=wavelength; angles are of incidence and diffraction. Use of hand held gratings in class. Interference.

3. 07.07.2011Lect. 5, gratings&light, 07.07.20113 Spectra Blue light is closer to grating “zero order” Multiple orders, m. Each  2 has a color associated with it.  1 the same for all colors (incident light). The entrance slit restricts all light to one angle (otherwise, the output makes no sense). Wavelength of known lines will be slightly greater or less depending on the relative motion of the emitting object toward us. Called the Doppler shift.  =v/c. Motion toward us makes a blue shift (negative): motion toward us is defined as negative, away, as positive.

4. 07.07.2011Lect. 5, gratings&light, 07.07.20114 Emission lines from gases. Pure gases that are excited generate isolated emission lines with no light in between Hot objects that are not pure gases emit a spectrum called “black body” radiation that is continuous, including all colors of the rainbow, as well as light at shorter and longer wavelengths than the eye can see. The emission lines sometimes form regular patterns, especially in the case of hydrogen. Balmer observed these in 1885. He found a mathematical relationship in terms of wavelength: 1/ =R[(1/n 1 ) 2 - (1/n 2 ) 2 ] R is the Rydberg constant, 109,000 cm -1. If he assigned n1 to be 2 and assigned each line (n2) to integers 2,3,4, …he found that he could exactly calculate the wavelengths of all the lines. In 1913, Bohr derived this equation from first principles, just as Newton did for Kepler’s empirical laws of the Solar System.

5. 07.07.2011Lect. 5, gratings&light, 07.07.20115 Theory of atomic spectra Narrow lines from pure gases imply that specfic energy levels are involved. Bohr built a model for hydrogen in which electrons (negative) orbited protons (postive) under an inverse square force (electric field, but of the same form as the gravitational force). More tightly bound electrons are closer in and have more negative energy (“bound”). When an electron is removed, it is “free”. If an electron goes from a more distant orbit to a smaller orbit, the atom is in a more negative total energy state (potential energy) and some energy has to be released to balance that change. Light is emitted as a result. The energy of the light is just the energy difference of the levels involved: E=E(start)-E(end), E=h  hc/  ev  x10 -12 g-cm 2 /sec 2 =  x10 -12 ergs

6. 07.07.2011Lect. 5, gratings&light, 07.07.20116 Absorption Lines If an electron in a bound atomic energy level interacts with an incoming photon of exactly the right energy, the photon will be absorbed and the energy will go into increasing the energy of the electron (making it less tightly bound, in a outer electron orbit). Energy is conserved. The electron will then spontaneously decay to an inner orbit (lower total energy, more negative, more tighly bound), producing positive, balancing energy by emitting a photon of the same energy and wavelength as the one initially absorbed. ONLY discrete energies can lead to absorption or emission from bound levels.

7. 07.07.2011Lect. 5, gratings&light, 07.07.20117 Stellar and Interstellar Absorption Lines In general, black body radiation produces photons of a wide range of energy, including higher energies for hotter objects. These photons can then be absorbed by atoms or ions (nuclei without a full set of electrons) that are between us and the black body (star), in discrete energies corresponding to energy separations. There are other means of continuous energy emission, such as “Bremstrahlung”, acceleration of electrons by passing protons in hot gases, and synchrotron emission (radiation from high energy electrons, beamed by special relativistic effects).

8. 07.07.2011Lect. 5, gratings&light, 07.07.20118 Units Atoms are of order 10 -8 cm in size, or 1 Angstrom. The energies between energy levels in atoms are typically a few electron volts, which corresponds to photon energies of 1000A to 10,000A, or 10 -5 to 10 -4 cm. The latter is 1 micron or 10 -3 mm.

9. 07.07.2011Lect. 5, gratings&light, 07.07.20119 1.Two stars orbit with a period of 50 years. They are each observed to move in circles around the center of mass of the system. The radii of the orbits are in the ratio 2/1. They are 8 arcsec apart and have a common parallax of 0.38 arcsec. a)What is the separation in AU? (21AU) b)What is the total mass of the system? (3.2 solar masses). c)What are the individual masses? (1.1 and 2.1) d)What is the velocity of the massive star in its orbit? e)What is the velocity of the second star?

10. 07.07.2011Lect. 5, gratings&light, 07.07.201110 2. Two black holes orbit each other. The total mass is 10,000 solar masses and the masses are in the ratio of 2/1. The period of the orbit is 1000 years. What is the total separation?(4.6 AU) 3. Two galaxies orbit each other. Each has about 10 11 solar masses, 1/5 in stars and 4/5 in dark matter. They are 100 kpc apart. What is the period? (7x10 9 years). How many orbits will they complete in the life of the Universe?

11. 07.07.2011Lect. 5, gratings&light, 07.07.201111