In the laboratory, one of the l;ines of sodium is emitted at a wavelength of 590.0 nm. In the light from a particular galaxy, however, this line is seen at a wavelength of 602.0 nm. Calculate the distance to the galaxy, assuming that Hubble’s law holds and that the Doppler shift of Eq 37-36 applies.
Thus, the distance of the galaxy is.
The relativistic Doppler shift formula is:
Light of wavelength 590.0 nm is observed to be 602.0 nm. Therefore, the speed of the source can be obtained from the equation.
The Hubble’s law is:
Therefore, the distance of the galaxy as calculated using the Hubble’s law will be:
Hence, the distance of the galaxy is.
Will the universe continue to expand forever? To attack this question, assume that the theory of dark energy is in error and that the recessional speed of a galaxy a distance from us is determined only by the gravitational interaction of the matter that lies inside a sphere of radius centered on us. If the total mass inside this sphere in, the escape speed from the sphere is (Eq.13.28).(a) Show that to prevent unlimited expansion, the average density inside the sphere must be at least equal to
(b) Evaluate this “critical density” numerically; express your answer in terms of hydrogen atoms per cubic meter. Measurements of the actual density are difficult and are complicated by the presence of dark matter
Question: Due to the presence everywhere of the cosmic background radiation, the minimum possible temperature of a gas in interstellar or intergalactic space is not 0 K but 2.7 K. This implies that a significant fraction of the molecules in space that can be in a low-level excited state may, in fact, be so. Subsequent de-excitation would lead to the emission of radiation that could be detected. Consider a (hypothetical) molecule with just one possible excited state. (a) What would the excitation energy have to be for 25% of the molecules to be in the excited state? (Hint: See Eq. 40-29.) (b) What would be the wavelength of the photon emitted in a transition back to the ground state?
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