Question 102 - (a) 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.
Answer 102 - (a) Approximately v = Zc / 137 = (79 / 137) c = 0.5766 c or 57.66 % of the speed of light. (b) Approximately A x A = 1 - Z x Z / 18769 = 1 - 79 x 79 / 18769 = 0.667 then A = 0.817. 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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ENGINEERING ECONOMY - EXAMPLE 7.1 : In engineering economy, the future value of first year is FV = PV (1 + i). For second year it is FV = PV (1 + i) (1 + i). For third year it is FV = PV (1 + i) (1 + i)(1 + i) where FV = future value, PV = present value, i = interest rate per period, n = the number of compounding periods. By induction, what is the future value of $1000 for 5 years at the interest rate of 6 %?
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Question 112 - In quantum computing, let the amplitude A = a | 0 > + b | 1 >, | a | | a | + | b | | b | = 1. Find the values of b if A = 0.8 | 0 > + b | 1 >.
Question 80 - Liquid octane has a density of 703 kilograms per cubic metre and molar mass of 114.23 grams per mole. Its specific heat capacity is 255.68 J / (mol K). (a) Find the energy in J needed to increase the temperature of 1 cubic metre of octane for 1 Kelvin. (b) At 20 degree Celsius, the solubility of liquid octane in water is 0.007 mg / L as stated in a handbook. For a mixture of 1 L of liquid octane and 1 L of water, prove by calculations that liquid octane is almost insoluble in water.
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