Homework problems

1	A helium atom finds itself momentarily in this arrangement. Find the direction and magnitude of the force acting on the right-hand electron. The two protons in the nucleus are so close together (~1 fm) that you can consider them as being right on top of each other.	√
2	The helium atom of problem 1 has some new experiences, goes through some life changes, and later on finds itself in the configuration shown here. What are the direction and magnitude of the force acting on the bottom electron? (Draw a sketch to make clear the definition you are using for the angle that gives direction.)	√
3	Suppose you are holding your hands in front of you, 10 cm apart. (a) Estimate the total number of electrons in each hand. (b) Estimate the total repulsive force of all the electrons in one hand on n all the electrons in the other. (c) Why don't you feel your hands repelling each other? (d) Estimate how much the charge of a proton could differ in magnitude from the charge of an electron without creating a noticeable force between your hands.	√
4	Suppose that a proton in a lead nucleus wanders out to the surface of the nucleus, and experiences a strong nuclear force of about 8 kN from the nearby neutrons and protons pulling it back in. Compare this numerically to the repulsive electrical force from the other protons, and verify that the net force is attractive. A lead nucleus is very nearly spherical, and is about 6.5 fm in radius.	√
5	The subatomic particles called muons behave exactly like electrons, except that a muon's mass is greater by a factor of 206.77. Muons are continually bombarding the Earth as part of the stream of particles from space known as cosmic rays. When a muon strikes an atom, it can displace one of its electrons. If the atom happens to be a hydrogen atom, then the muon takes up an orbit that is on the average 206.77 times closer to the proton than the orbit of the ejected electron. How many times greater is the electric force experienced by the muon than that previously felt by the electron?	√
6	The nuclear process of beta decay by electron capture is described parenthetically in section 2.6. The reaction is p+e- → n+ν. (a) Show that charge is conserved in this reaction. (b) Conversion between energy and mass is discussed in an optional topic in section 2.8. Based on these ideas, explain why electron capture doesn't occur in hydrogen atoms. (If it did, matter wouldn't exist!)	S
7	234Pu decays either by electron decay or by alpha decay. (A given 234Pu nucleus may do either one; it's random.) What are the isotopes created as products of these two modes of decay? [Note that in printed edition 2.1 of this book, I inadvertently left the atomic numbers off of the last row of the periodic table. The ones from Th to Lr run from 90 to 103.]