646 Table 850 (continued) 



MATTER AND ENERGY 



equilibrium constant of an ideal gas reaction, d ■ log K/dT= Q/RT 2 ) he derives a T of 

 io 12 °K. Milne yields another solution. If n = no. of protons (electrons) present per cm 3 

 at statistical equilibrium, then n = 0.96 X io 18 T*X i ~ (2 - 3SXI ° 12)/r - 



We have the following picture : As T rises, molecules will be ionized and finally all 

 dissociated to atoms ; then the atoms become ionized with finally a proton-electron gas. 

 At some very high temperature P + E — » radiation sets in. Milne's equation shows that 

 at T = io 10 this reaction is practically complete. As T rises yet higher the birth of matter 

 will commence and we see that T = io 12 , the equilibrium density of matter becomes equal 

 to 1.34 X io 10 g/cm 3 . T = io 12 corresponds to enormous densities for both matter and 

 radiation. Enormous voltages (9 X io 8 volts) may give the attainment of such reactions. 



Compton effect. — X rays are supposed to consist of streams of energy quanta. While 

 each quantum carries the energy equivalent to hv, one may also specify each of these 

 photons (light units) by the momentum which, according to the theory of quanta, is equal 

 to hv/c. When this photon collides with a free or loosely bound electron there is an inter- 

 change of both energy and momentum in accordance with the laws of conservation of 

 energy and of momentum. Consequently the photon suffers a recoil in one direction with 

 loss of momentum, while the electron moves off in another direction with added momentum. 

 The decrease in momentum of the scattered X-ray photon corresponds to an increase in 

 wave length. (Dushman, Gen. Elec. Rev., 33, 334, 1930.) 



De Broglie phase waves. — De Broglie was led to the conception that associated with a 

 particle of mass m« (rest mass, zero velocity) and velocity v, there is a wave motion of 

 wave length given by 



X = h V 1 — if/f/mov = h/vioV 



for small values of v; c is the velocity of light. The theory of relativity gives as the total 

 energy, E, of a particle of mass Wo 



E = nuc 2 / V 1 —v'/c = mc 



with m the mass for velocity v. According to the quantum theory, the frequency associated 

 with E is given by E/li. Hence the phase velocity or velocity of the individual waves con- 

 stituting the group is given by 



u = p\ = mc 2 /mv = c 2 /v. 



The value of h is 6.55 X io" 7 erg/sec. For a mass of 1 g moving at 1 cm/sec. the asso- 

 ciated wave length is 6.55 X io" 27 cm — too small to be measured at present. Wave lengths 

 io" 10 to io" T cm are measurable with crystal lattices. With de Broglie's assumption we 

 would expect corpuscular motion to exhibit phenomena like those associated with light 

 waves under conditions where the momenta of the particles are of the order of magnitude 



Smithsonian Tables 



