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1. What are the wavelengths for the Balmer lines (n→2 transitions)? What are the wavelengths of the Lyman (n→1) transitions in the limit n→∞? 1 1 91.16nm 2 2 n2 n1 1 1 H 1 1 91.16 2 2 656.3 nm 2 3 H 1 1 91.16 2 2 486.2 nm 2 4 1 1 Balmer limit 1 1 91.16 2 364.64 nm 2 This means any photon with <364.64 can completely remove an electron in the n=2 level from the atom. 1 Lyman limit 1 1 91.16 2 91.16 nm 1 A photon with wavelength less than this can ionize H no matter what level the electron is initially in. 2. Doppler shifts a) Typical stars in the solar neighbourhood have velocities ~30 km/s. What is the size of their Doppler shift? This is much less than the speed of light, so v r / c 0.0001 0.05nm at visible wavelengths. At visible wavelengths, l~500 nm, so the wavelength shift is 0.04 nm. To resolve this wavelength difference, a grating must have nN 12500 b) Extragalactic objects (mostly galaxies and quasars) are strongly redshifted due to the expansion of the Universe. The most distant object currently known is quasar SDSS1148+5251, with z=6.42. Since z is not small, we have to use the full expression: vr ( z 1) 2 1 c ( z 1) 2 1 7.42 2 1 7.42 2 1 0.964 c) Barnard’s star has a very high proper motion of ~88 km/s. The spectrum of Barnard’s star shows the H absorption line at a wavelength of 656.044 nm. What is its full space velocity? In the laboratory: 4 c 1 1 4 2 2 e n2 n1 656.3 nm 3 1 1 1 1 91.176 2 2 nm 2 3 So the radial velocity is: vr c c 656.044 656.3 656.3 117 km/s And the full space velocity is: v vr2 v 2pec 146 km/s 3. Pulsars are rapidly spinning neutron stars which beam light in opposite directions. They have huge magnetic fields of 108 – 1012 gauss. How large is the Zeeman splitting? eB 2me c 1.60 10 19 C 1010 G 2 9.1110 31 kg 2.998 108 m/s 9.32 1011 Hz The frequency of visible light is about 6x1014 Hz. So even in this strong magnetic field the Zeeman splitting is only about a 0.1% effect. 4. The star Rigel has a spectral type B8Ia and a magnitude V=0.14. What is its distance? From the Hipparcos HR diagram, this spectral class corresponds to: M V 6.5 0.5 So Dstar 10 10 m M 1 5 0.14 6.5 1 5 213 50 pc