Useful formulae:
1 Angstrom = 10-10 m
E=h n
where
n is frequency and h=6.626 x 10-34 Joules
1 Joule = 1 kg m2 / s2
1 eV = 1.6 x 10-19 Joules
l= c/n
Brightness = Luminosity / 4 pD2
lmax=2.9 x 10-3m K /
T (Wien's Law)
v/c = D l/
l0
where
v is the radial velocity of the object (the ambulance or a star)
moving away or towards us
where
l0 = lrest
and where
D l is the
doppler shift in wavelength
lshifted-
lrest
c=300,000 km/s
Vega is a bright nearby star. Let's say that the wavelength at
which Vega emits most of its light is 3052 Angstroms.
a)
What is the surface temperature of Vega? [Hint: use Wien's Law and
be sure to label your answer with the proper unit]
The sun has a surface temperature of 5860 K.
b) What is the wavelength
at which the
sun emits most of its light?
c)What can you say about the color of the sun compared to the color of Vega?
Rigel and Betelgeuse are two bright stars in the constellation Orion.
(FYI, you can see a picture of the constellation on p. 40 of the text,
or look up at night towards the West before 8:30 pm.) Betelgeuse is red, and Rigel is blue.
a)Which star is hotter?
If two stars were located at the
same distance, and if the blue star appeared
fainter than the red star.
b)Which star, the blue star or the red star, would have a smaller radius?
Explain your answers!
Using data from Table F.1 and F.2 in the Appendix section of your text "The Cosmic Perspective,"
we see that
a Centauri is a binary star i.e. it
consists of two stars orbiting around each other. Inspecting the
second star of the pair a Centauri
(spectral type K0 V), it has a
luminosity that is just over half the luminosity of the sun
(L
a Centauri
=0.53
Lsun).
Using additional data from the table
which
star will appear brighter to us on Earth: the Sun or
a Centauri (spectral type K0 V)?
How much brighter will that star appear?
In the hydrogen atom, a transition of the electron from one energy level to another energy level has a rest wavelength of 4340 Angstroms. Suppose you see this line in the spectrum of a star with a wavelength of 4342 Angstroms.
a) Is the star moving away or moving towards the Earth?
b)What is the velocity of that star? (Hint: use the Doppler effect formula)
Imagine a hydrogen atom, with an electron in an "excited" state. The
electron absorbs light of wavelength 4340 Angstroms and is further
excited.
a)What is the energy of
this wavelength of light? in units of
Joules and in units of eV?
b) Is energy gained or lost by the electron when it absorbs this light?
c)How much energy is lost or gained by the electron?
d)If the electron originally has an energy of 10.2 eV, what is its energy in eV after absorbing the photon of light at 4340 Angstroms?