ch44 kho tài liệu bách khoa

1 Conservation of momentum requires that the gamma ray particles move in opposite directions with momenta of the same magnitude Since the magnitude p of the momentum of a gamma ray particle is related to its energy by p = E/c, the particles have the same energy E Conservation of energy yields mπc2 = 2E, where mπ is the mass of a neutral pion The rest energy of a neutral pion is mπc2 = 135.0 MeV, according to Table 44-4 Hence, E = (135.0 MeV)/2 = 67.5 MeV We use the result of Problem 83 of Chapter 38 to obtain the wavelength of the gamma rays: λ= 1240 eV ⋅ nm = 1.84 ×10−5 nm = 18.4 fm 67.5 × 10 eV We establish a ratio, using Eq 22-4 and Eq 14-1: Fgravity Felectric 2 −11 −31 Gme2 r 4πε 0Gme2 ( 6.67 × 10 N ⋅ m C )( 9.11×10 kg ) = = = ke r e2 ( 9.0 ×109 N ⋅ m2 C2 )(1.60 ×10−19 C ) = 2.4 ×10−43 Since Fgravity