Principles of Geochemistry
Homework Set #1: Atomic structure and chemical composition of crust and selected
rocks
Due Date: January 23, 2008 at the start of class
1) What is the energy in a quantum of radiation having a wavelength of 4500 Å?
Please report your answer in Joules and electron volts. To what frequency would
this correspond in Hertz? In what part of the electromagnetic spectrum does this
photon belong? Is a photon of radiation with a frequency of 93.1 MHz more or
less energetic than the one at 4500 Å? Please show all work and be careful with
your units.
2) The fissioning of a 235U atom yields 200 MeV of energy. How many atoms of
235U must the Arkansas Nuclear One plant of Entergy Co. fission in order to
generate the energy equal to that of lifting a beer stein from the bar table to your
mouth? Assume that the average glass beer stein has a mass of 450 g and the
distance from the table to your mouth is 15 in.
3) Calculate the radii of the first, second, and third “permitted” electron orbits of
hydrogen in angstroms. What is the diameter of the hydrogen atom in the ground
state? Show work.
4) Calculate the force on an electron in the hydrogen atom due to the electrostatic
field of the nucleus at the distance of the first Bohr orbit. Now calculate the
gravitational force between the nucleus and this electron. What is the ratio of
these forces?
5) Calculate the frequency, wavelength, and wavenumber of the Hβ line of the
Balmer series for hydrogen. This line is emitted in the transition from n2=4 to
n1=2. You may assume that the nucleus has infinite mass is not moving. Show all
work.
6) How many electrons can be accommodated in orbitals having the principal
quantum number of 4? Write out the complete set of quantum numbers associated
with all of these electrons.
7) Write out the electronic formulas to describe Co, S, Br, V, and Cu (i.e.
1s22s22p6…). Explain the expected valences of these elements based on their
electronic configurations in the ground state.
8) Fe has four stable isotopes. Use an appropriate reference to find the relative
abundance of each of these isotopes. Calculate the mean atomic weight of Fe from
these data in atomic mass units.
9) Calculate the concentration of Al and Si in orthoclase feldspar. Is there more Si
per mol in quartz or in orthoclase feldspar? How many atoms of Si are there in
each mineral?
10) A solution of Al2(SO4)3 contains 500 µmol/L of Al3+. How many grams of SO42-
does it contain per liter?
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