Nuclear engineering formulas

Ax — average atomic mass of the element; found using Equation 1 when the element contains multiple isotopes; units are typically atomic mass units (amu),

γᵢ — atomic fraction of isotope i; tells you what fraction of the atoms are isotope i; found from the isotope abundance, usually given as a percentage and converted to a decimal,

Aᵢ — atomic mass of isotope i; the mass of the specific isotope; found on a chart of nuclides or from the nuclear data provided in the problem,

Σᵢ — sum over all isotopes or species i; means you add the contribution from every isotope present,

Ax = ∑ᵢ γᵢAᵢ — average atomic mass of an element; multiply each isotope’s atomic fraction by its atomic mass and add all of the isotope contributions together,

wₓ — weight fraction of element x; represents the fraction of the total mass of a compound that comes from element x; calculated from the chemical formula using Equation 2,

n — number of atoms of element x in the chemical formula; found by looking at the subscript of x in the chemical formula,

Ax — atomic mass of element x; found on the periodic table,

m — number of atoms of element y in the chemical formula; found by looking at the subscript of y in the chemical formula,

Ay — atomic mass of element y; found on the periodic table,

nAx — total mass contribution of element x in the chemical formula; multiply the number of x atoms by the atomic mass of x,

mAy — total mass contribution of element y in the chemical formula; multiply the number of y atoms by the atomic mass of y,

wₓ = nAx/(nAx + mAy) — weight fraction of element x in a compound; divide the mass contribution of x by the total mass of the compound,

wᵢ — weight fraction of isotope i; represents the fraction of the total mass that comes from isotope i; found from the isotope abundance when the abundance is given by mass or weight,

Aᵢ — atomic mass of isotope i; mass of the specific isotope; found on a chart of nuclides or in the problem,

Σᵢ — sum over all isotopes; means you perform the calculation for every isotope and add the results together,

Ax — average atomic mass of the element; the overall average atomic mass after accounting for the weight fractions of all isotopes,

Ax = [∑ᵢ(wᵢ/Aᵢ)]⁻¹ — average atomic mass from weight fractions; calculate wᵢ/Aᵢ for every isotope, add the values, then take the inverse of the result,

Nᵢ — number density of isotope i; number of atoms of isotope i per unit volume; typically units of atoms/cm³ or atoms/m³; this is what the equation is solving for,

γᵢ — atomic fraction of isotope i; fraction of all atoms that are isotope i; found from the isotope abundance, usually given as a percentage and converted to a decimal,

ρₓ — mass density of the element or material; mass per unit volume; given in the problem or a reference table; typically g/cm³ or kg/m³,

Nₐ — Avogadro’s number; number of particles in one mole; 6.022 × 10²³ particles/mol; a constant,

Ax — average atomic mass of the element; found using Equation 1 if multiple isotopes are present; can also be provided in a problem or reference table,

Nᵢ = γᵢρₓNₐ/Ax — number density of isotope i; uses the isotope’s atomic fraction, material density, Avogadro’s number, and average atomic mass to determine the number of atoms of that isotope per unit volume,

ρᵢ — mass density of isotope i; the mass of isotope i per unit volume; typically units of g/cm³ or kg/m³; this is what the equation calculates,

wᵢ — weight fraction of isotope i; fraction of the material's total mass that comes from isotope i; given in the problem or calculated from isotope information,

ρₓ — total mass density of the element or material; mass per unit volume of the entire material; given in the problem or a reference table,

ρᵢ = wᵢρₓ — mass density of isotope i; multiply the isotope’s weight fraction by the total material density to determine the density contributed by that isotope,

Nᵢ — number density of isotope i; number of atoms of isotope i per unit volume; typically atoms/cm³ or atoms/m³; this is what the equation calculates,

wᵢ — weight fraction of isotope i; fraction of the total mass belonging to isotope i; given in the problem or calculated from isotope abundance information,

ρₓ — total mass density of the material; mass per unit volume; given in the problem or a reference table,

Nₐ — Avogadro’s number; 6.022 × 10²³ particles/mol; a constant,

Aᵢ — atomic mass of isotope i; mass of the specific isotope; found on a chart of nuclides or given in the problem,

Nᵢ = wᵢρₓNₐ/Aᵢ — number density of isotope i; uses the isotope’s weight fraction, total material density, Avogadro’s number, and isotope atomic mass to calculate how many atoms of that isotope exist per unit volume,

γᵢ — atomic fraction; find from isotope abundance; convert percentage to decimal,

wᵢ — weight fraction; find from mass/isotope abundance information or calculate from the material composition,

Aᵢ — isotope atomic mass; find on the chart of nuclides,

Ax — average atomic mass; find on the periodic table for a naturally occurring element or calculate with Equation 1/3 when isotope information is provided,

ρₓ — material mass density; find in the problem statement or a reference table,

Nₐ — Avogadro’s number; constant; 6.022 × 10²³ particles/mol,

n — number of atoms of an element in a chemical formula; find from the chemical formula subscript,

m — number of atoms of the other element in a chemical formula; find from the chemical formula subscript,

Nᵢ — number density; usually the variable you are solving for; units are atoms/volume,

ρᵢ — isotope mass density; usually the variable you are solving for in Equation 5; units are mass/volume,