ASTR 100 (McGaugh)
Homework #5 solutions

Chapter 10, Problem # 1

In order of increasing wavelength:

e) the x-rays in your dentist's office
a) the output of an ultraviolet tanning lamp
d) a beam of red light
c) leakage from a very cheap microwave oven
b) a radio broadcast of Saturday's big football game

Chapter 10, Problem # 4

a) An atom in the ground state cannot produce emission lines, because emission lines are produced when an electron in an atom drops from a higher (excited) state to a lower state. But when an atom is in the ground state, all its electrons are in their lowest possible states, thus there is no lower energy state for them to drop into.

b) From part a) we see that emission lines will occur only if atoms are in an excited state (ie only if one or more of their electrons are in higher states than the ground (lowest) state). An outside source of energy such as radiation or collisions with other atoms is needed to raise the electrons from the ground state to a higher energy state. Thus, emission-line glows will occur in nebulae near hot stars where the star's radiation and collisions with other atoms in the gas heated by the star cause the atoms to be in excited states. Emission lines will not be observed from the cold gas in interstellar space, since there is no energy source there to excite the atoms.

Chapter 11, Problem # 1

We know that the Sun's energy does not come from chemical burning, because the energy produced by the Sun is too great to be the result of this process. In 1871, Herman von Helmholtz showed that you would need to burn the enormous amount of 7000 kg of coal per hour per square meter of the Sun's surface to reproduce the Sun's energy output. Furthermore, if the Sun was in fact burning chemical fuel, it would have used up all it's mass as fuel in only a few thousand years. This is far to short a lifetime for the Sun since we have determined that the Earth is more than 4 billion years old and the Sun must have existed at least as long as the Earth. The fact that the Sun's energy output far exceeds that which could be accounted for by chemical burning led scientists to believe that its energy source must be something different.

Scientist infer that the Sun's energy source is the nuclear fusion reactions of the proton-proton cycle, because this is the mechanism which best accounts for the observed properties of the Sun. First, nuclear fusion of the material within the Sun is efficient enough at producing energy to account for the Sun's observed enormous energy output. The amount of mass present in the Sun would be sufficient fuel, if used in fusion reactions, to make the Sun shine for a lifetime of several billions of years. Further, scientists were able to measure the Sun's composition using spectroscopy and found that the Sun was made primarily of hydrogen and helium. This is what one would expect if the proton-proton cycle was fueling the Sun, since hydrogen is the fuel needed for the proton-proton cycle and helium is produced by that reaction. Also, scientists have observed neutrinos coming from the Sun. These particles are another product of nuclear fusion and thus further evidence that fusion is the process which produces the Sun's energy. Finally, scientists have been able to make theoretical models of the Sun, based on their observations of its size and composition, which show that the conditions in the Sun's center would allow nuclear fusion to occur.

The Sun's energy is generated mostly at its center because this is the only place within the Sun where the pressure and temperature are high enough for nuclear fusion to occur. A temperature of at least 10 million K is necessary for nuclear fusion to occur. It is incredibly difficult to create a fusion reaction on earth, because all known materials melt at only a few thousand degrees. Thus, there is no known material one could use to make a container to hold the hydrogen at the high temperature necessary for the fusion reaction.

Chapter 11, Problem # 8

The Sun has a mass of 1.99 × 1030 kg.

The total mass of the planets in the Solar system is:
3.30 × 1023 kg + 4.87 × 1024 kg + 5.98 × 1024 kg + 6.44 × 1023 kg + 1.90 × 1027 kg + 5.69 × 1026 kg + 8.76 × 1025 kg + 1.03 × 1026 kg + 1.5 × 1022 kg = 2.67 × 1027 kg

So, MSun / Mplanets = (1.99 × 1030 kg) / (2.67 × 1027 kg) = 745

So, the Sun is nearly 750 times more massive than all the planets put together.

Since the Sun is essentially a giant ball of gas formed by the gravitational collapse of much of the material in the solar nebula, its composition is approximately the same as that of the solar nebula (ie it is primarily hydrogen and helium). The Earth, on the other hand, was formed from whatever materials were able to condense out of the Solar nebula at the temperatures found at it's distance from the Sun. These included the magnesium-, calcium-, and iron-rich silicate minerals which are the basic materials of rocks.

The most abundant element in the solar system is Hydrogen.
The second-most abundant element in the solar system in Helium.

Chapter 12, Problem # 9

Two stars lie on the main sequence in different parts of the H-R diagram:

a) The star which is farther toward the left and top of the diagram is larger.
b) The star which is farther toward the left and top of the diagram is more luminous.
c) The star which is farther toward the left and top of the diagram is more massive.
d) The star which is farther toward the left and top of the diagram is hotter.
e) Part c), the relative masses of the stars, could not be determined just from their location on the H-R diagram if both stars were not on the main sequence.