Homework hint: All problems in the text have answers at the back of the book! Some problems require just a written response, while others ask you to calculate something. Please write up all answers clearly, completely, and as succinctly as possible. You can work with others, but your final answers must be written up on your own.

a) Why then is Mercury less dense, when its iron core is larger in proportion to its size than Earth's (see Fig. 2.17)?

b) Jupiter's density implies that it does not have a large iron core. Why doesn't it?

** Question 2.** a) Calculate the average bulk density of
the planets Venus, Mars, and the Moon in the same way that it is done
for Earth in Question 2.1 on page 32. The data that you need and the correct
answers can be found in Tables A1 and A2 in the back of the book.

b) Assuming that the three objects are made from uncompressed iron,
with a density of 7900kg/m^{3}, and rock (assume
2500-3000kg/m^{3}), would you expect iron cores larger or
smaller (relative to the object's radius) than Earth's in each case?
Compare with Fig. 2.17 and discuss.

c) Estimate the mass of the
Earth's crust, its mantle, and its core. Use reasonable numbers given
in Fig. 2.4 and state your assumptions!

** Question 3.** On page 66, the author states the
radioactive elements U and Th are concentrated in the Earth's
crust. What about Potassium (K), the most important heat-generating
element? Note that unlike U and Th, where all isotopes are radioactive,
K has both stable and radioactive isotopes. Drawing information from
the chapter, determine if K is concentrated, and if so,
where. Consider the Earth's core, mantle, and crust. Back up your
argument quantitatively.

** Question 4.** Check out the spidergram plot in
Fig. 2.28 on page 350.

a) Please explain why the elements Rb, K,
Na, and Zn are depleted in the mantle.

b) Some of these elements
are not depleted in the crust - from your answer to question 2c,
estimate what the comparable curve for (crust + mantle) would look like
on Fig. 2.28. Are these elements depleted in the outer half of the
Earth?

** Question 5.** This problem will explore why there is
no natural radioactive Aluminum 26 on Earth (or anywhere else in the
Solar System! - see box 2.7 on pg. 64).

a) First, from Table 2.2,
we estimate that the Earth is about 1% Aluminum by weight. Given that
the weight of an Aluminum 27 atom is 4.5*10^{-26}kg, roughly
how many Aluminum 27 atoms does Earth have?

b) Now assume that the
Earth originally had an equal number of Aluminum 26, which is
radioactive with a 0.73 million year halflife. About how many
halflives would it take for only 1 part in 1000 of the ^{26}Al
to remain? How much time is this?

c) About how much time did it
take for all ^{26}Al to decay away to nearly the last atom?
Can you say how long it took the last atom to decay? Compare these
numbers to the age of the Earth and discuss.

** Question 6.** How much heat was released in massive
collisions with early Earth? Go to the Solar System Collisons
program and simulate some major collisions!

a) Start with a 1 cm
rocky particle moving at 20 km/s. Start making a table recording i)
what happens, ii) how often it happens, and iii) energy released if
appropriate. Now increase the size to 10 cm and run again. Continue to
increase the impactor size by factors of 10 until you reach 9999
km.

b) Work out an estimate for the amount of energy released by
radioactivity in the Earth over its entire history. Use today's
present heat production rates given on page 64, and multiply your
final answer by 3 to correct for the fact that there was more
radioactive heating of Earth in the past. What size impactor releases
a similar amount of energy? To convert energy between Megatons of TNT
and the SI unit Joules, use 1 Megaton = 4.2*10^{15} Joules.

** Question 7.** Go to the Scientific Notation
program. Run it until you are sure that you can do this type of
problem in your sleep (or on an exam!). What happens when you get a
problem right?

b) Do the same with the Working with
Equations program. Check off the equations for v, g, E, and H
which we may meet in this class; E gives the amount of energy
released in the impacts of Question 6. What is in the help file? If
you have trouble doing either of these problems, be sure to talk to
me or the grader.