star.le.ac.uk /~ mbu / lectures.html

1. Lecture course slides can be seen at: • http://www.star.le.ac.uk/~mbu/lectures.html

2. Ch. 40 Nuclear size and Shape • Nuclei exist bcse strong nuclear force overcomes electrostatic repulsion force over close distances inside nucleus • Energetics & stability of nucleus depends on number of protons & electrons inside Z, the number of protons, the atomic number of the atom. N, the number of neutrons. A, the mass number of the nucleus, the total number of nucleons, A=N+Z. From scattering experiments, nuclei are roughly spherical with radius proportional to number of nucleons A1/3 where R0=1.2-1.5 femtometres = 1.2-1.5x10-15m

3. Ch. 40 Nuclear size and Shape • Volume is proportional to A, so density constant • Nucleus looks like a liquid drop • For light nuclei N~Z • For heavier nuclei the number of neutrons increases • The extra uncharged neutrons act to stabilize heavy nuclei from repulsive electrostatic forces

4. Nuclear density Estimate the density of nuclear matter. Density: M = mass of proton/neutron = 1.67x10-27kg x A R0= 1.5x10-15m Find density = 1.18x1017kg m-3

5. Ch. 40 The radioactive decay process b-Decay: either a neutron turns into a proton, with emission of an electron (b-) or proton turns into a neutron (b+): So A remains same, Z changes by +/-1 g-Decay: excited nucleus decays into lower energy state via emission of a photon. A and Z constant a-Decay: tends to occur in heavier elements, which can become more stable by reducing their size N and Z decrease by 2, A decreases by 4

6. Ch. 40 Mass and binding energy • Binding energy per nucleon varies with mass number A • For small A (<50) • Steady increase in number of nearest neighbours as A increases • Therefore an increase in no. of bonds per nucleon • For medium A (>50) curve ~flat • Additional nucleons too far away • Nuclear forces saturate • Only nearest neighbours important • For large A (>200) • Coulomb repulsion force becomes large • Nucleus unstable, spontaneous fission • Fusion of nuclei to the left of Fe • Fission to the right

7. Ch. 40 Mass and binding energy • This plot of mass difference per nucleon v A is the negative of the binding energy curve • The rest mass per nucleon for both very heavy (A>200) and very light (A<20) nuclides is more than for nuclides of intermediate mass • Thus, energy is released when a very heavy nucleus breaks up into two lighter nuclei (fission) • Or when two light nuclei fuse together to form a heavier nucleus (fusion)

8. Fission • Very heavy nuclei can spontaneously break apart, placing limit on size of nucleus and number of possible elements • Some heavy elements can be induced to fission by capture of a neutron • Fission of 235U (right): • Nucleus excited by capture of neutron • Splits into two daughter nuclei & emits more neutrons (avg 2.5) • Coulomb repulsion force drives fragments apart • Thermal energy released (exothermic) • Self-sustaining reaction (chain reaction) possible • Big bang with nasty isotopes • Or control in reactor by keeping number of viable neutrons per reaction to 1

9. Fusion • Two light nuclei fuse to form a heavier nucleus • Energy per unit mass > fission • Abundance of light elements holds great promise for producing power from fusion • Fewer dangers than fission (chain reactions, nasty isotopes) • Bcse of coulomb repulsion, kinetic energies ~1MeV needed to get deuterium and tritium close enough for nuclear forces to become effective & fusion to occur • Scattering more likely • Particles must be heated to high enough temps (~108K) for fusion to occur as a result of thermal collisions • Temps like this found in stars • At this temp, gas is a plasma of +ve ions and e- • Confining plasma difficult • Done by star’s high gravity • Barely achieved in any fusion reactor to date