## Units of Reactivity

Mathematically, reactivity is a **dimensionless number**, but various units can express it. The most common units for **research reactors** are units normalized to the **delayed neutron fraction (e.g.,, cents and dollars)** because they exactly express a departure from prompt criticality conditions.

The most common units for **power reactors** are units of **pcm** or **%ΔK/K**. The reason is simple. Units of **dollars are difficult to use** because the normalization factor, **the effectively delayed neutron fraction**, significantly **changes with the fuel burnup**. In LWRs, the delayed neutron fraction decreases with fuel burnup (e.g.,, from **β _{eff} = 0.007** at the beginning of the cycle up to

**β**at the end of the cycle). This is due to isotopic changes in the fuel. It is simple.

_{eff}= 0.005**Fresh uranium fuel**contains only

^{235}U as the fissile material. Meanwhile, during fuel burnup, the importance of fission of

^{239}Pu increases (in some cases up to 50%). Since

^{239}Pu produces significantly fewer delayed neutrons (

**0.0021**for thermal fission), the resultant core delayed neutron fraction of a multiplying system decreases (the weighted average of the constituent delayed neutron fractions).

β_{core}= ∑ P_{i}.β_{i}

## %ΔK/K

The unit of reactivity in **percent** of the effective multiplication factor. For example, the subcriticality of **k _{eff} = 0,98** equals

**-2%**in units of

**%ΔK/K**. Since this is a

**very large amount of reactivity**, these units are usually used to express significant reactivity like power defects,

**xenon worth**, the

**integral worth of control rods,**or

**shutdown margin**. This unit is inappropriate for operational changes that affect the effective multiplication factor because these changes are of the lower order.

**k _{eff} = 0.99** ρ = (keff – 1) / keff = -0.01 ρ = -0.01 * 100% =

**-1 %**