94 Chapter 3. The molecular dance[[Student version, December 8, 2002]]
case where the potential energy is a constant, this formula reduces to the Maxwell distri-
bution. More generally, for manyinteractingmolecules in equilibrium the probability for
molecule number 1 to have velocityv 1 and positionx 1 ,and so on, equals a constant times
e−E/kBTd^3 v 1 d^3 v 2 ...d^3 x 1 d^3 x 2 ...(Equation 3.26), where nowEis the total energy forall
the molecules.
5.Rates: The rates of many simple chemical reactions depend on temperature mainly via the
rapidly varying Arrhenius exponential factor, e−Ebarrier/kBT(Equation 3.27).Further reading
Semipopular:
Probability: (Gonick & Smith, 1993)
Genetics: (Gonick & Wheelis, 1991)
Schr ̈odinger’s and Gamow’s reviews: (Schr ̈odinger, 1967), (Gamow, 1961)
Polymers: (deGennes & Badoz, 1996)
Intermediate:
Probability: (Ambegaokar, 1996)
Molecular theory of heat: (Feynmanet al.,1963a,§39.4)
History of genetics: (Judson, 1995)
Technical:
X-ray mutagenesis experiment: (Timof ́eeff-Ressovskyet al.,1935)