QUANTUM BIOLOGY - EXAMPLE 33.7 : (a) In a DNA of a living cell, the quantum information available in the bases guanine (G) and thymine (T) are | G > = | 110 > and | T > = | 010 > respectively. Calculate | G > - | T >. (b) In a living biological cell, the step time for random walk of an electron is t. The localization time of an electron is T. If i is the geometric average of T and t, find log T as a function of t and i.
QUANTUM BIOLOGY - ANSWER 33.7 : (a) | G > - | T > = | 110 > - | 010 > = | 100 >. (b) Geometric average of T and t is the square root of (T x t) = i. Then log i = 0.5 log (Tt), log (Tt) = log T + log t = 2 log i, log T = 2 log i - log t. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; firstname.lastname@example.org; http://kangchuentat.wordpress.com.
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QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.1 : As an approximation, let v = Zc / 137 where v is the radial velocity for 1 s electron of an element, c is the speed of light, Z is the atomic number. For gold with Z = 79, find the radial velocity of its 1 s electron, in term of c and percentage of the speed of light. (b) As an approximation, let A x A = 1 - Z x Z / 18769 where A is the ratio of the relativistic and non-relativistic Bohr radius. Find the value of A.