PHGN 422: Nuclear Physics Lecture 11: Introduction to Radioactive Decay Prof. Kyle Leach
September 27, 2016 Slide 1
PHGN
422: NUCLEAR PHYSICS
Last Week...
• We cannot solve the S.E. exactly for the nucleus • An approximation of the nuclear potential by a Woods-Saxon
potential and a spin orbit interaction • That forms the basis for the shell model of the nucleus • The shell model was able to describe our observed magic
numbers, as well as predict spins and parities for nuclei.
Radioactive Decay: is the process by which a nucleus of an unstable atom decreases its total energy by spontaneously emitting radiation (we’ll define that in a couple slides).
Characterization of Radioactive Material Henri Becquerel’s discovery inspired Marie and Pierre Curie to investigate the phenomena further. • They found that the mineral
pitchblende was more active than uranium, and concluded that it must contain different radioactive substances • From this, they discovered
polonium and radium, both of them more radioactive than uranium.
Example 1: Application Abundance of Uranium Problem: Age of uranium ore We start in the mountains in Mongolia. One of our students is busy digging for gold (trying to strike it rich!), when they come across a sample of uranium ore. In that sample, they notice that there is quite a lot of lead. To simplify things, they assume that all of the 208 Pb in the sample came from the decay of 238 U. They also find that the ratio of 208 Pb/238 U. How old is the ore? Adapted from Thornton and Rex, Example 12.17
Example 2: Application Carbon Dating Problem: Dating of a buried Roman emperor Another student is an avid archaeologist and decides to spend their summer abroad in the UK. While trying to dodge a large rolling boulder, the student stumbles upon some human remains. Based on its location and surrounding artifacts, they suspect that it is from a Roman emperor. They take the sample to the lab, and it is determined that the carbon ratio 14 C/12 C is 1.10 × 10−12 . Are the remains old enough to be from an ancient Roman emperor? Adapted from Thornton and Rex, Example 12.18
So far, we have only considered the simple case where the nucleus decays via one mode, to one final state. However, in nature this is extremely unlikely. There is nearly always some probability of multiple decay modes taking place simultaneously. These decays are characterized by their partial half-lives and branching ratios. Let’s consider a more complex decay on the board:
Next Class... Reading Before Next Class • Radioactive Decay Supplement and Chapter 6 in Krane
Next Class Topics • Statistics of radioactive decay (continued) • The quantum theory of radioactive decay • Production and decay radioactivity • Complex decay chains
