Nuclear reactions Chapter 17

Standard Describe nuclear reactions and identify the properties of nuclei undergoing them.

Nucleons Source: Griffith, Physics of Everyday Phenomena

Nuclear Reactions Parent  Daughter(s) + “particles”

Exponential Decay N(t) = N 0 e –t/  N(t) = number of nucleons at time t N 0 = number of nucleons at time 0  = lifetime –N/N 0 = 1/e at time  Half-life t 1/2 = ln(2)  =  –N/N 0 = 1/2 at time t 1/2

Exponential Decay N(t) = N 0 e –t/  Decay rate is directly proportional to N –dN/dt Probability of decay is unchanging “Rate constant” r = 1/  Nuclei do not “grow old” = –(–1/  ) N 0 e –t/  = (1/  ) N(t)

Decay Timescale 50% chance a nucleus will decay in one half-life Source: Griffith

Nuclear Stabilities Source: Hodgson et al., Introductory Nuclear Physics

Nuclear Reaction Types Alpha decay Beta decay Gamma emission Fission Fusion Spontaneous processes release energy –Rest mass decreases  E = –  mc 2

Conservation laws nucleon number –actually baryon number –actually quark number electric charge

Main Radioactive Emissions Source: Griffith

Alpha Decay Nucleus emits an alpha particle = 2p + 2n (helium-4 nucleus) Daughter nucleus has Z – 2, N – 2, A – 4

Question After alpha decay, the atomic number of a nucleus is A.larger B.smaller C.the same as before.

Question After alpha decay, the mass number of a nucleus is A.larger B.smaller C.the same as before.

Beta decay n= neutron p + = proton e – = electron (beta particle) n  p + + e – Problem: e – energy varies Maximum energy  mc 2 Violates conservation of energy?

The neutrino “little neutral one” must be neutral must have small mass Must have very little interaction with other particles Observed in reverse beta decay + p +  n + e +

Beta decay n= neutron p + = proton e – = electron (beta particle) e = electron anti-neutrino e –, e escape, p + remains in nucleus Daughter has same A, Z + 1, N – 1 n  p + + e – + e

Beta + decay p +  n + e + + e n= neutron p + = proton e + = positron (anti-electron) (  + ) e = electron neutrino e +, e escape, n remains in nucleus Daughter has same A, Z – 1, N + 1

Electron Capture p + + e −  n + e n= neutron p + = proton e − = electron (  ) e = electron neutrino e escapes, n remains in nucleus Daughter has same A, Z – 1, N + 1

Question After beta decay, the atomic number of a nucleus is A.larger B.smaller C.the same as before.

Question After beta decay, the mass number of a nucleus is A.larger B.smaller C.the same as before.

Gamma Emission Excited nucleus emits a high-energy photon Occurs only after another decay type Source: Griffith

Question After gamma emission, the atomic number of a nucleus is A.larger B.smaller C.the same as before.

Board Work 4.Find the daughters of the following nuclear decays: a. 239 Pu   + b. 99 Mo   +

Question Which kind of atomic nuclei tend to undergo alpha decay? A.Nuclei with large atomic number Z. B.Nuclei with too many neutrons. C.Very light (low Z) nuclei. D.Nuclei with too many protons.

Question Which kind of atomic nuclei tend to undergo beta decay? A.Nuclei with large atomic number Z. B.Nuclei with too many neutrons. C.Very light (low Z) nuclei. D.Nuclei with too many protons.

Binding Energy Source: Georgia State U., Hyperphysics fission fusion

Fission Nucleus breaks into two large fragments plus several neutrons Source: Griffith

Fission Chain Reaction Source: Griffith

Criticality Reaction self-sustaining if each fission on average induces another Critical mass depends on geometry, moderation, reflection, many other factors

Spent Fuel Hazards Source: Cohen, B. L. Rev. Mod. Phys. 1977, 49, 1–20.

Fissile Nuclei Required for reactors and bombs Fission started by absorption of thermal neutrons Only fissile nuclei are U-233, U-235, and Pu-239 U-235 is less than 1% of natural uranium (rest is U-238)

Plutonium Breeding Source: Griffith

Fusion Two nuclei combine to make a larger nucleus Neutrons usually released as well

Question What sort of nucleus releases energy by fission? A.Nuclei lighter than iron. B.Nuclei about as heavy as iron. C.Nuclei heavier than iron.

Summary Nuclei contain positive protons and neutral neutrons. Nuclear stability is a balance between electrostatic repulsion and the attractive strong force.

Summary Radioactive atoms can emit alpha particles, beta particles, and gamma rays. Nuclei can also split apart (fission) and combine (fusion). Reaction types depend on nuclear characteristics.