Reactor Theory (Nuclear Parameters) DOE-HDBK-1019/2-93REACTIVITYExample:Calculate the reactivity in the reactor core when k_{eff} is equal to 1.002 and 0.998.Solution:The reactivity for each case is determined by substituting the value of k_{eff}into Equation (3-5).r k_{eff } 1k_{eff}1.002 11.0020.001996r k_{eff } 1k_{eff}0.998 10.9980.0020UnitsofReactivityReactivity is a dimensionless number. It does not have dimensions of time, length, mass, or anycombination of these dimensions. It is simply a ratio of two quantities that are dimensionless.As shown in the calculation in the previous example, the value of reactivity is often a smalldecimal value. In order to make this value easier to express, artificial units are defined.By definition, the value for reactivity that results directly from the calculation of Equation (3-5)is in units of Dk/k. Alternative units for reactivity are %Dk/k and pcm (percent millirho). Theconversions between these units of reactivity are shown below.1%D kk0.01D kk1 pcm 0.00001D kkAnother unit of reactivity that is used at some reactors is equivalent to 10^{-4}Dk/k. This unit ofreactivity does not have a unique name. Special units for reactivity that do have unique namesare dollars and cents. These units and their applications will be described in a later chapter.Rev. 0NP-03Page 19