QUANTUM BIOLOGY - EXAMPLE 33.5 : (a) In the measurement of the number of photons received by a plant during photosynthesis, quantum meter is used. At 8 AM, 11 AM, 12 PM, 2 PM and 4 PM of the same day, the measured readings of the meter are 10, 70, 60, 120 and 120 units. Find the mode, median and min of the readings of the quantum meter. (b) Microtubule is used to carry information in a cell. If the cross-sectional area of the microtubule has a diameter of 25 nanometers, find the volume of the microtubule of 1 nanometer in height. State the assumption of calculation.
QUANTUM BIOLOGY - ANSWER 33.5 : (a) Mode = 120 (2 readings, greater than others with 1 reading). Median = 70 (since 70 is the middle, when the values are rearranged orderly as 10, 60, 70, 120, 120). Min = (sum of readings) / (number of readings) = (10 + 70 + 60 + 120 + 120) / 5 = 380 / 5 = 76. (b) Assumption : Microtubule is a cylinder. Let V = 3.142 x h x d x d / 4 where V = volume, d = diameter, h = height. Then V = 3.142 x h x d x d / 4 = 3.142 x n x 25 n x 25 n / 4 = 490.9375 n x n x n = 4.909375 x 10^2 x 10^(-9) x 10^(-9) x 10^(-9) = 4.909375 x 10^(-25) meters, where ^ is the symbol of power, n is nano or 10^(-9). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.9 : When an algebraic product is defined on the space, the Lie bracket is the commutator [x,y] = xy - yx according to Lie algebra in mathematics. If [p,x] f(x) = px f(x) - xp f(x), p = -ih d / dx, find the value of [p,x] in term of i and h.
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Chemical Engineering Material Balance - Three hundred gallons of a mixture containing 75.0 wt % ethanol and 25 wt % water (mixture specific gravity = 0.877) and a quantity of a 40.0 wt % ethanol - 60 wt % water mixture (specific gravity = 0.952) are blended to produce a mixture containing 60.0 wt % ethanol. The specific gravity of a substance is the ratio of density of a substance compared to the density of water. The symbol of weight percent is wt %. (a) Estimate the specific gravity of the 60 % mixture by assuming that y = mx c where y is wt % ethanol, x is mixture specific gravity. Values for m and c are constants. (b) Determine the required volume of the 40 % mixture.
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