Really Understand Beta Decay
Crack this and you will have covered:
Radioactive decay, Carbon Dating, Feynman Diagrams, Anti-Particles..all in one go. Now that is SMART!
Introduction
Beta decay is the nuclear process where a Proton decays to a Neutron or vice vera This happens with emission of an electron (beta particle). This makes the nucleus more stable but has the effect of changing the chemical nature of the atom.
Question 1: What is the equation for Beta Plus decay?
Make a guess at proton decays to neutron and beta plus. Check the Baryon number 1 goes to1 correct. But when check Lepton number 0 goes to -1, Wrong. Ah remember we need to add a lepton to the RHS.Guess number two add an electron neutrino. Now the Baryon and Lepton numbers balance. Finally we check the charge and that balences too. We have the correct answer!
Question 2: Draw a Feynman Diagram of Beta Plus decay
Use the same equation you derived for Question 1 above. Remember a Feynman diagram has the shape of the letter H for two particles in and two out. BUT in our Answer ! above it is one in and three out so the third particle is flipped. The only thing missing from our equation is the exchange particle. Rember Beta decay is a WEAK nuclear reaction so the particle is a W+ Boson and we know it is plus because it carries away the positive charge of the incoming proton to decay into the beta plus, JOB DONE!
Question 3: Draw a Feynman Digram of Beta Plus Decay at Quark Level
We can see from the quark properties in the data sheet opposite that a proton must be uud to make a charge of +1 and that the neutron must be udd.
Therefore we know that an up quark of the proton decays to a down quark to form a neurton. So the Feynman diagram is very similar to the one in Q3 above except the p is replaced by u and the n by p. As to be edited below:
Question 4: Describe Carbon Dating including the decay of Carbon 14 to Nitrogen
Again use the equation from Question 1, however we know that Nitrogen has one more proton than Carbon, so the decay must be Beta Minus. So just swap everything. Neutron goes to Proton plus Beta Negative plus and Anti Neutrino.
Summary
By just using the information suppliedin the question text, the data sheet and a very basic understanding of the form of the physics we’ve been able to answers four different questions with precision and understood a large part of the Nuclear Physics part of the sylabus.