Astronomy 2, Spring 2007
Homework set 5, due May 22 .
1. The inverse
square law for light. Sirius, Procyon, and Betegeuse are three stars prominent
in the sky now. Sirius has an
apparent magnitude m of -1.4, an
absolute magnitude M of +1.45,
and a luminosity (power output) L
of 26 times the sunŐs luminosity or 26Lsun. Procyon has m = +0.4, M = +2.68, and L = 7.7Lsun, and Betelgeuse has m = +0.45, M = -5.41, and L = 40,000Lsun.
(a) Arrange these stars in order of (1) increasing apparent
brightness, (2) increasing power output, and (3) increasing distance. Explain your answers.
(b) How many times brighter does Sirius appear to be in the
sky than Betelgeuse? How much more power does Betelgeuse radiate than
Sirius? How do you reconcile these
two numbers?
2. Atoms and spectral lines. Shown below is the energy level diagram of a hypothetical
element called Delerium. Only the
three bound levels shown below are of any interest in this atom. The energy of
the excited levels relative to the ground state is shown on the left in
arbitrary energy units E. The wiggly line represents ionization energy, so
transition G is an ionization. Answer the following, explaining your answers clearly.
(a) Which transition would emit the highest energy photon?
(b) Which transition would absorb the longest wavelength
photons?
(c) How many absorption lines would be seen in an absorption
spectrum of Delerium, if these are the only energy levels involved? Do transitions like G produce sharp absorption
lines?
(d) Calculate the ratios of the wavelengths of the
absorption lines.
3. Blackbody
radiation. The closest star other than the sun, Proxima Centauri, has a
surface temperature of about 3000K. The sunŐs is twice as high, and the
supergiant Rigel is about twice as hot as the sun. Explain your answers.
(a) On the same graph, sketch the continuum (blackbody)
output curves of these three stars.
Clearly label the axes and identify each curve. Which star has the longest wavelength
of maximum emission? Which has the shortest?
(b) Arrange the stars in order of increasing energy output
per unit area.
(c) What is the ratio of energy output per unit area of
Rigel to Proxima Centauri?