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Friday, March 10, 2017 4:26

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This semester I am teaching a class in Oakland University’s Honors College called *The Making of the Atomic Bomb*, based on Richard Rhodes’ book by the same name. The class is a mixture of nuclear physics, a history of the Manhattan Project, and a discussion about World War II (today we discuss Pearl Harbor). I became interested in this topic from the writings of Cameron Reed of Alma College here in Michigan.

The Honors College students are outstanding, but they are from disciplines throughout the university and do not necessarily have strong math and science backgrounds. Therefore the mathematics in this class is minimal, but nevertheless we do a two or three quantitative examples. For instance, Chadwick’s discovery of the neutron in 1932 was based on conclusions drawn from collisions of particles, and relies primarily on conservation of energy and momentum. When we analyze Chadwick’s experiment in my Honors College class, we consider the head-on collision of two particles of mass *M*_{1} and *M*_{2}. Before the collision, the incoming particle *M*_{1} has kinetic energy *T* and the target particle *M*_{2} is at rest. After the collision, *M*_{1} has kinetic energy *T*_{1} and *M*_{2} has kinetic energy *T*_{2}.

Intermediate Physics for Medicine and Biology examines an identical situation in Section 15.11 on Charged-Particle Stopping Power.

The maximum possible energy transfer

Wcan be calculated using conservation of energy and momentum. For a collision of a projectile of mass_{max}M_{1}and kinetic energyTwith a target particle of massM_{2}which is initially at rest, a nonrelativistic calculation gives

One important skill I teach my Honors College students is how to extract a physical story from a mathematical expression. One way to begin is to introduce some dimensionless parameters. Let *t* be the ratio of kinetic energy picked up by *M*_{2} after the collision to the incoming kinetic energy *T*, so *t* = *T*_{2}/*T* or, using the notation in IPMB, *t* = *W _{max}*/

The goal is to unmask the physical behavior hidden in this equation. The best way to proceed is to examine limiting cases. There are three that are of particular interest.

__ m much less than 1__. When

__ m much greater than 1__. When

__ m equal to 1__. When

A mantra I emphasize to my students is that equations are not just things you put numbers into to get other numbers. Equations tell a physical story. Being able to extract this story from an equation is one of the most important abilities a student must learn. Never pass up a chance to reinforce this skill.

Source: http://hobbieroth.blogspot.com/2017/03/my-honors-college-class-making-of.html