1 Chapter 31 Nuclear Physics and Radioactivity

2 1. Nuclear Structure a)Proton - positive charge - mass x 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 x 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 A X is needed.

5 e) Atomic mass unit, u Define: Mass of 12 C = 12 u Then, 1 u = 1.66 x kg = MeV/c 2 m p = u m n = u In chemistry and biology, 1 dalton (Da) = 1 u

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

7 2. Nuclear force and stability a)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 b) Symmetry c) Coulomb repulsion - Pauli exclusion principle: N=Z gives maximum stability considering only nuclear force -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 b) Mass defect From special relativity, adding energy increases mass:

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

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

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

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

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

16 Potential energy diagram for two halves of a large nucleus: fission releases energy Fission: 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 a)  - decay - ejection of 4 He nucleus - transmutation: element changes - Energy released (KE of , daughter, energy of photon) Use atomic masses for P, D, 4 He (electrons balance): For 238 U, 234 Th, 4 He, E = 4.3 MeV  -decay

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

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

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

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

23 e) Neutrino, - postulated by Pauli in 1930 to account for missing energy in  -decay - observed in 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 a) Activity Activity is the number of decays per unit time, or where N represents the number of nucleii present. For a random process, the activity is proportional to N: This gives (by integration) where N 0 is the number of nuclei at t = 0. Units: 1 Bq (becquerel) = 1 decay/s 1 Ci (curie) = 3.7 x Bq (activity of 1 g radium) is the decay constant

25 b) Half-life Exponential decay: For a given time interval, the fractional decrease in N is always the same: 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 a) Carbon dating - based on the reaction: T 1/2 = 5730 years - 14 C/ 12 C ratio constant in atmosphere due to cosmic rays - living organisms ingest atmospheric carbon; dead matter doesn’t - ratio of 14 C/ 12 C in matter gives time since death Equilibrium ratio: 1/8.3 x ==> 1 g C contains 6 x atoms of 14 C ==> Activity of 1g C (at eq’m) = 0.23 Bq = A 0 ==> Activity of 1g C (time t after death) = A= A 0 e - t

28 b) Dating ancient rocks Age equation: