vp2 k Tmvp2 k Tm21.38 x 1016ergK293 K1.66 x 1024g2.2 x 105cmsec1 m100 cm2200msecReactor Theory (Neutron Characteristics)DOE-HDBK-1019/1-93NEUTRON FLUX SPECTRUMRev. 0Page 35NP-02In the thermal region the neutrons achieve a thermal equilibrium with the atoms of the moderatormaterial. In any given collision they may gain or lose energy, and over successive collisionswill gain as much energy as they lose. These thermal neutrons, even at a specific temperature,do not all have the same energy or velocity; there is a distribution of energies, usually referredto as the Maxwell distribution (e.g., Figure 2). The energies of most thermal neutrons lie closeto the most probable energy, but there is a spread of neutrons above and below this value.MostProbableNeutronVelocitiesThe most probable velocity (v ) of a thermal neutron is determined by the temperature of thepmedium and can be determined by Equation (2-13) .(2-13)where:v=most probable velocity of neutron (cm/sec)pk=Boltzman's constant (1.38 x 10erg/ K)-16T=absolute temperature in degrees Kelvin ( K)m =mass of neutron (1.66 x 10grams)-24Example:Calculate the most probable velocities for neutrons in thermal equilibrium with theirsurroundings at the following temperatures. a) 20 C, b) 260 C.Solution:a)Calculate the most probable velocity for 20 C using Equation (2-13).
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