The 0 meson is a particle that has a rest energy of 135.0 MeV (see Table 32.3).

The π0 meson is a particle that has a rest energy of 135.0 MeV (see Table 32.3). It lives for a very short time and then decays into two g-ray photons: π0 → γ + γ. Suppose that one of the g-ray photons travels along the 1x axis.

Concepts:

(i) How is the energy E of each g-ray photon related to the rest energy E0 of the π0 particle?

(ii) How can the frequency and wavelength of a photon be determined from its energy?

(iii) How is the total linear momentum of the photons related to the momentum of the π0 particle, and what is the momentum of each particle?

Calculations:

If the π0 is at rest when it decays, find

(a) The energy (in MeV),

(b) The frequency and wavelength,

(c) The momentum of each g-ray photon.

When considering the biological effects of ionizing radiation, the concept of biologically equivalent dose is especially important. Its importance lies in the fact that the biologically equivalent dose incorporates both the amount of energy per unit mass that is absorbed and the effectiveness of a particular type of radiation in producing a certain biological effect. Problem 55 examines this concept and also reviews the notions of power (Section 6.7) and intensity (Section 16.7) of a wave. Problem 56 illustrates the decay of a particle into two photons, and provides a review of the principles of conservation of energy and conservation of momentum.

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Table 32.3 Some Particles and Their Properties Rest Energy (MeV) Particle Antiparticle Symbol Lifetime (s) Family Particle Symbol Self Boson" Photon Stable 3 x 10-25 w- W+ 8.04 × 104 Z° Gluons Graviton Z° Self 9.12 × 104 3 x 10-25 e- or B- or B+ Lepton Electron 0.511 Stable e+ Muon 2.2 x 10-6 με 105.7 Tau 1777 2.9 x 10-13 <2 x 10-6 Stable Electron neutrino Ve Muon neutrino <0.19 Stable Tau neutrino <18.2 Stable Hadron Mesons Pion 139.6 2.6 x 10-8 +t т" Self 135.0 8.4 X 10-17 Kaon к* K- 493.7 1.2 × 10-8 K° ко 497.6 Eta Self 547.3 <10-18 Baryons Proton 938.3 Stable Neutron 939.6 886 п Lambda Ло 1116 2.6 X 10-10 Σ" Sigma 1189 8.0 x 10-11 1193 7.4 X 10-20 1197 1.5 X 10-10 Ω Ω Omega 1672 8.2 x 10-1"