Chapter 31

1. Chapter 31 Nuclear Physics and Radioactivity

2. 1. Nuclear Structure • Proton - positive charge - mass 1.673 x 10-27 kg ≈ 1 u b) Neutron - discovered by Chadwick (student of Rutherford) - hypothesized to account for mass of atom - discovered with scattering experiments - zero charge - mass 1.675 x 10-27 kg ≈ 1 u - mass of neutron ≈ mass of proton + mass of electron - neutron can eject electron to form proton, but it’s not a proton and an electron

3. c) Nucleon - constituent of nucleus (neutron or proton) d) Nomenclature A - number of nucleons (atomic mass number) Z - number of protons N - number of neutrons A = Z + N Symbol for nucleus of chemical element X:

4. Examples: Since Z determines the element (X), only AX is needed.

5. e) Atomic mass unit, u Define: Mass of 12C = 12 u Then, 1 u = 1.66 x 10-27 kg = 931.5 MeV/c2 mp = 1.00727 u mn = 1.008665 u In chemistry and biology, 1 dalton (Da) = 1 u

6. e.g. 35Cl, 37Cl (65%, 35%), 12C, 13C, 14C (99%, 1%, 0.01%) f) Isotopes; nuclei with the same Z, different N g) Nuclear size and density Close-packed - constant density - Volume proportional to atomic number (A) - Since V = 4/3 πr3, A prop. to r3 - r prop. A1/3 - r ≈ (1.2 x 10-15 m) A1/3 = 1.2 fm A1/3 - density of neutron star = 100 million tonne/cm3

7. 2. Nuclear force and stability • Strong nuclear force • one of the fundamental forces • holds protons together in spite of Coulomb repulsion • short range: ~ fm (zero for longer range) • only adjacent nucleons interact • acts equally between n-p, n-n, p-p

8. - Pauli exclusion principle: N=Z gives maximum stability considering only nuclear force c) Coulomb repulsion b) Symmetry • long range; all protons interact (only adjacent nucleons feel nuclear force) • - repulsion increases with size -- neutron excess needed for stability • - above Z = 83 (Bi) stability not possible; larger elements decay emitting radioactivity

9. 3. Mass defect and binding energy a) Binding energy energy required to separate constituents of nucleus

10. From special relativity, adding energy increases mass: b) Mass defect

11. Example: 4He (alpha particle) Compare ionization potential for H atom: 13.6 eV

12. Masses usually tabulated for neutral atoms (including atomic electrons) - Can use atomic masses if electrons balance: c) Atomic electrons

13. - determines stability - for 4He, BE = 28 MeV so BE/nucleon = 7 MeV d) Binding energy per nucleon increase in nearest neighbors increase in Coulomb repulsion dominates

14. Energy released For a given number of nucleons, - if BE/nucleon increases - mass defect increases - total mass decreases - energy released Fusion Fission

15. Fusion: Potential energy diagram for nucleons: fusion releases energy Energy (high temperature in the sun) required to push nuclei together against the Coulomb force.

16. Fission: Potential energy diagram for two halves of a large nucleus: fission releases energy May occur spontaneously, or be induced by neutron bombardment

17. 4. Radioactivity • spontaneous decay of nucleus • releases energy to achieve higher BE/nucleon • mass of parent > mass of products

18. - ejection of 4He nucleus - transmutation: element changes a) - decay - Energy released (KE of , daughter, energy of photon) Use atomic masses for P, D, 4He (electrons balance): -decay For 238U, 234Th, 4He, E = 4.3 MeV

19. - ejection of electron - governed by weak nuclear force - transmutation b)  - decay - Energy released, as KE of electron Use atomic masses for P, D, and add one electron mass: - decay For 234Th and 234Pa, E = 0.27 MeV

20. Other modes of beta decay - ejection of positron - electron capture

21. - emission of a photon - no transmutation - accompanies  - decay, fission, neutron decay c)  - decay

22. - sequential decays to an eventual stable nucleus • 4 separate series (A can only change by 4) d) Decay series 238U -> 206Pb 235U -> 207Pb 232Th -> 208Pb 237Np -> 209Bi (not obs’d)

23. postulated by Pauli in 1930 to account for missing energy in -decay e) Neutrino,  • observed in 1956 • mass ~ zero (< ~ eV) (standard model predicts non-zero mass) • could account for missing mass in universe • zero charge • interacts only by weak nuclear force (difficult to detect)

24. 5. Radioactive decay rate; activity Activity is the number of decays per unit time, or a) Activity where N represents the number of nucleii present. For a random process, the activity is proportional to N:  is the decay constant This gives (by integration) where N0 is the number of nuclei at t = 0. Units: 1 Bq (becquerel) = 1 decay/s 1 Ci (curie) = 3.7 x 1010Bq (activity of 1 g radium)

25. Exponential decay: For a given time interval, the fractional decrease in N is always the same: b) Half-life Define half-life as the time for activity to reduce by 1/2:

26. Using the exponential can be expressed so

27. 6. Radioactive dating - based on the reaction: T1/2 = 5730 years a) Carbon dating - 14C/12C ratio constant in atmosphere due to cosmic rays - living organisms ingest atmospheric carbon; dead matter doesn’t - ratio of 14C/12C in matter gives time since death Equilibrium ratio: 1/8.3 x 1011 ==> 1 g C contains 6 x 1010 atoms of 14C ==> Activity of 1g C (at eq’m) = 0.23 Bq = A0 ==> Activity of 1g C (time t after death) = A= A0e-t

28. b) Dating ancient rocks Age equation: