Blackbody Radiation and Wien's Law
1. Solve Wien's Law for T, substitute in the values for
wavelength. With the temperature you obtain, look on the HR diagram for
the corresponding spectral class.
(a) 9656 K Class A; (b) 19,313 K Class B; (c) 5267.2 K Class G; (d)
2317 K Class M
2. Substitute the temperatures into Wien's Law and obtain the
wavelengths of the peak emission. Look up on a chart of the EM spectrum
which region the wavelength falls into.
(a) 289.7 cm radio; (b) 3.62x10^{4} cm infrared; (c)
1.93x10^{5} cm ultraviolet;
(d) 1.65x10^{7} cm Xray
Extension:
No astronomical objects are as cold as 0.001 Kelvin. The radio emission
we observe is produced by electrons moving in magnetic fields (this is
called synchrotron radiation).
Bigger than a Breadbox?
Using the equation: distance = velocity x time,
Cygnus: 9.14x10^{14} km; Crab: 4.46x10^{13} km; Tycho:
6.96x10^{13} km; SN1006: 9.37x10^{13} km
The supernova occurred in the year 1604 and is known as Kepler's
supernova. It was observed and documented by the astronomer Johannes
Kepler.
A Teaspoonful of Starstuff
Using the equation: mass = density x volume,
We are given that the volume of interest is 5 cm^{3}. So what
is the density of each of the objects? Density equals mass/volume, and the
volume of a sphere is ^{4}/_{3} πr^{3}, where r is the radius of the sphere.
Plugging in the values for each of the types of stars, we find that our
teaspoon of the Sun would contain 7.0 grams; of the white dwarf would
contain 9.5x10^{6} grams; of the neutron star would contain
3.3x10^{15} grams. By looking up the density of water, air, and
iron, you can calculate that each would be 5.0 grams,
6.5x10^{3} grams, and
39.4 grams, respectively.
Crossing the Event Horizon
1. Using the Schwarzschild equation, we input the mass of
Jupiter (1.9x10^{27} kg), the Gravitational constant (G =
6.67x10^{11} m^{3}/kgsec) and the velocity of light
(3x10^{8} m/sec) to see that the event horizon of a Jupitermass
black hole would occur at 2.96 meters.
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