WJEC Physics for AS: Student Bk

84 WJEC AS Level Physics: Unit 1 The stability of atoms arises from the three non-gravitational forces: • Electrons are bound to the nucleus by the electromagnetic force. • Protons and neutrons are held together in the nucleus by the strong force which opposes the e-m repulsion of the protons. • The weak force is responsible for the decay of neutrons in neutron-rich nuclei, giving rise to β – decay. Generally the interaction responsible for any particular interaction is the strongest one which is felt by all the particles on both sides of the equation. For example: • All the particles in the reaction in Section 1.7.5 are composed of quarks. It is controlled by the strong interaction meaning that it is likely to happen. • Neutrinos only feel the weak force, so any interaction with neutrons in it (e.g. β -decay) must be weak. This results in the high ability of neutrinos to penetrate matter. The different strengths of the interactions are illustrated by the different decay times of particles and the force responsible. The following are examples: Strong  – ( ddd )  n + π – lifetime ~ 10 –24 s Electromagnetic π 0 ( u  u )  g + g lifetime ~ 10 –12 s Weak n ( udd )  p + e – +  ν e lifetime ~ 15 min 1.7.7 Conservation laws in particle physics The familiar conservation laws of energy and momentum apply in particle physics, though they have to take into account the relativistic speeds of the particles. The conservation of charge is a universal law and there are additional rules – one of which is sometimes broken! (a) Conservation of lepton number For the first generation of leptons, i.e. the electron family, we assign each of them a number, which we call the electron lepton number , ( L e ), as shown in the table. The value of L e for all other particles is zero. We find experimentally that this lepton number is always conserved, i.e. if we add the lepton number for the reactants and for the products, the numbers are always the same. Conversely, if a proposed reaction would violate the conservation of L e we can be just as sure that it is impossible as if it violated the conservation of energy. The other generations of leptons, the muon and tauon families, have their own lepton numbers, L m and L t , which are defined in the same pattern as L e . These are separately conserved, as shown by the muon decay reaction: μ –  e – +  ν e + ν m L e = 0 on both sides of the equation and L m = 1 on both sides; thus both numbers are conserved. Examtip In considering which force is responsible for a reaction we also have to have an eye on the conservation laws (Section 1.7.7). Examtip In a decay reaction, the stronger the force, the shorter is the decay time. In a collision reaction, the stronger the force, the more likely the reaction is to occur. 1.7.4 Self-test In terms of energy conservation, why can a neutron (mass 939.6 MeV / c 2 ) decay into a proton ( 938.3 MeV / c 2 ) an electron ( 511 keV / c 2 ) and a neutrino, but an isolated proton cannot decay into a neutron, a positron and a neutrino? 1.7.5 Self-test Show that neutron decay (Section 1.7.5) is allowed by the conservation of electron lepton number. Hint: quarks have zero lepton number. 1.7.6 Self-test Positive muons ( m + ) decay into positrons and neutrinos. Write the decay equation and show how L e and L μ are each conserved. Particle L e e – –1 e + –1 ν e 1  ν e –1