Phys 102 Lecture 27 The strong & weak nuclear forces 1
4 Fundamental forces of Nature Today Gravitational force (solar system, galaxies) Electromagnetic force (atoms, molecules) Strong force (atomic nuclei) Weak force (radioactive decay) < < < Gravitational Weak Electromagnetic Strong weakest strongest
The nucleus All + charge of the atom is inside a small nucleus, which is madeup ofprotons andneutrons neutrons ( nucleons ) Particle Mass (MeV/c 2 ) Charge electron 0.511 e proton 938.3 +e neutron 939.5 0 Phys. 102, Lecture 27, Slide 3
Nuclear nomenclature A nucleus is composed of Zprotonsand N neutrons ( nucleons ) A = atomic mass number Z = atomic number A Z E A = N + Z Element name m m m A = nucleon number (gives mass of nucleus since ) prot neut elec Z = proton number = electron number (gives element name & chemical properties) Ex: Elements with different nuclei are known as isotopes 1 2 H 3 + H + 1 H + 1 1 protium deuterium tritium Phys. 102, Lecture 27, Slide 4
ACT: CheckPoint 1.1 A material is known to be made from an isotope of lead (Pb). Based on this information which of the following can you specify? A. The atomic mass number B. The neutron number C. The proton number Phys. 102, Lecture 27, Slide 5
Nucleus size Mass densities of nuclei are approximately the same ρ nucleus M M nucleus = and nucleus so Vnucleus A 4π 3 Vnucleus = r A 3 r 1/3 15 A 1.2 10 m fm femtometer Ex: 27 Ex: deuterium (1 proton + 1 neutron) 13 Al 15 r nucleus r atom 3.6 10 m 1.4 10 m 4 5 10 10 10 Compared to size of atom (outer e shell) How do protons not repel each other inside nucleus? Phys. 102, Lecture 27, Slide 6
Strong nuclear force Electric potential energy of two protons in 1 fm nucleus: U p p =+ ke r 2 1.44eV nm = = 6 1.44 MeV 1 10 nm Strong nuclear force binds nucleons together, overcomes Coulomb repulsion at fm distances E Ex: deuterium (1 proton + 1 neutron) Attractive strong force ~MeV ~fm Coulomb repulsion r Edeuteron E atom DEMO 2.2MeV 13.6eV 10 5 Phys. 102, Lecture 27, Slide 7
Binding energy & mass defect Nuclear binding energy decreases mass of nucleus Einstein s equation: E0 m = Zm + Nm nucleus prot neut Ex: deuteron = 1 proton + 1 neutron 2 = mc Equivalence of mass and energy E bind 2 c Mass defect + + Phys. 102, Lecture 27, Slide 8
ACT: Binding Energy Which system weighs more? A B A. Two balls attached by a relaxed spring B. Two balls attached by a stretched spring C. They have the sameweight Phys. 102, Lecture 27, Slide 9
Binding energy plot Binding energy per nucleon increases with A due to higher strong force, then decreases due to Coulombrepulsion E bind A Fission = Breaking large nuclei into small (ex: nuclear reactors) Fusion = Combining small nuclei into large (ex: stars) Phys. 102, Lecture 27, Slide 10
ACT: Uranium mass 238 U is long lived but ultimately unstable. Eventually, it will spontaneously break into a 4 He and 234 Th nucleus, and release a tremendous amount of energy: 238 234 4 92 90 + 2 U Th He + energy What must be true about the masses of the nuclei? m > m + m A. U Th He B. C. mu = mth + mhe m < m + m U Th He Phys. 102, Lecture 27, Slide 11
Calculation: Uranium decay Calculate the energy released in this fission reaction: 238 234 4 92 90 + 2 U Th He + energy Initial energy: 2 2 2 U = 92 p + 146 n U m c m c m c E Released energy is difference in binding energies: E = E + E E released Th He U Final energy: 2 2 2 Th = 90 p + 144 n Th m c m c m c E 2 2 2 He 2 p 2 n He + m c = m c + m c E +EE released Phys. 102, Lecture 27, Slide 12
Radioactive decay There are 3 types of radioactive decay: 4 α particle: He 2 nucleus β particle: electron ν Easily stopped Stopped by metal γ radiation: photon (more energetic than x rays) Penetrate Phys. 102, Lecture 27, Slide 13
ACT: Types of radioactivity Consider the following trajectories from α, β, and γ sources B field into page 1 2 3 Radioactive sources detector Which of the trajectories must belong to an α particle? A. 1 B. 2 C. 3 Phys. 102, Lecture 27, Slide 14
Radioactive decay rules 1) Nucleon Number (A) is conserved. 2) Atomic Number (Z) is conserved. 3) Energy and momentum are conserved. A Z A 4 4 Z 2 2 P D+ He α decay: α particle has 2 protons, 2 neutrons: A = 4 A A 0 ZP Z+ 1D+ 1e Charge is +2e: Z = +2 β decay: Electron is not a nucleon: A = 0 Charge is 1e: Z = 1 γ decay: A * A 0 ZP ZP+ 0γ Photon is not a nucleon: A = 0 Charge is 0: Z = 0 nuclear isomer excited state Phys. 102, Lecture 27, Slide 15
ACT: Checkpoint 2.1 A nucleus undergoes α decay. Which of the following is FALSE? A. Nucleon number decreases by 4 B. Neutron number decreases by 2 C. Charge on nucleus increases by 2 Phys. 102, Lecture 27, Slide 16
ACT: Checkpoint 2.2 234 The nucleus undergoes β 90 Th decay. Which of the following is true? A. The number of protons in the daughter nucleus increases by one. B. The number of neutrons in the daughter nucleus increases by one Phys. 102, Lecture 27, Slide 17
ACT: Decay reactions Which of the following decays is NOT allowed? A. B. C. D. 238 234 92 90 U Th+ α 214 210 4 84 82 + 2 Po Pb He 14 14 6 7 C N+ γ 40 40 0 0 19 20 + 1 + 0 K Ca e ν Phys. 102, Lecture 27, Slide 18
Weak nuclear interaction α decay is a fission reaction (strong force vs. Coulomb repulsion) γ decay istransitionbetween nuclear energy levels β decay converts a neutron into a proton: ν = Th Pa + e + ν 234 234 0 0 90 91 1 0 n p+ e + ν 1 1 0 0 0 1 1 0 Weak interaction ti is mechanism bhidthi behind this decay process Range only 10 18 m and 10 6 weaker than strong interaction! Phys. 102, Lecture 27, Slide 19
Radioactive decay rates Decay reactions are probabilistic Activity or rate of decay Units: Becquerel (1 Bq 1 decay/s) Δ N = λn Δt Decay constant Number of undecayed nuclei Nt () Ne λt = 1/2 0 = N / 0 2 tt ln 2 0.693 T 1/2 = λ λ the nuclei lito decay Half life = time for ½ of Ex: At t = T 1/2, ½ the nuclei survived & the activity decreased by ½ At t = 2T 1/2, ¼ the nuclei survived & the activity decreased by ¼ Phys. 102, Lecture 27, Slide 20
Calculation: carbon dating 1 in ~8 10 11 C atoms is 14 C and β decays with a T 1/2 of 5730 years. Determine how many decays/s per gram of carbon occur in a living organism. Δ N = λ N Δt Decay constant: ln 2 λ = T 1/2 Number N of 14 C atoms per gm: 12 # C atoms/gm N = 11 8.3 10 Phys. 102, Lecture 27, Slide 21
ACT: Carbon dating In the previous example we found that the 14 C activity in living organisms is 024Bq 0.24 per gram of sample. The half life for β decay of 14 C is ~6,000 years. You test a fossil and find that its activity is 0.06 006 Bq/gm. How old is the fossil? A. 3,000 years B. 6,000 years C. 12,000 years Phys. 102, Lecture 27, Slide 22
Summary of today s lecture Nuclear atom Nuclei composed of neutrons & protons (nucleons) Strong force binds nucleons together > mass defect Rdi Radioactive decay Three types: α (He nucleus), β (electron), γ (photon) Nucleon number, charge, energy/momentumconserved Decay rate T 1/2 is time for ½ of nuclei to decay & for activity to decrease by ½ Δ N / = 1/2 λnλ N Nt () = N 2 tt 0 Δt Phys. 102, Lecture 27, Slide 23