Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Law of mass action formula. The law of mass action also has implications in semiconductor physics. Regardless of doping, the product of electron and hole densities is a constant at equilibrium. This constant depends on the thermal energy of the system (i.e. the product of the Boltzmann constant, formula_20, and temperature, formula_21), as well as the band gap (the energy separation between conduction and valence bands, formula_22) and effective density of states in the valence formula_23 and conduction formula_24 bands. When the equilibrium electron formula_25 and hole formula_26 densities are equal, their density is called the "intrinsic" carrier density formula_27 as this would be