Question 105 - In a rigid rotor model in quantum chemistry, the moment of inertia I is given by an Equation E as I = Ma x La x La + Mc x Lc x Lc = m x L x L, where m = (Ma x Mc) / (Ma + Mc) and L = La + Lc, m is the reduced mass, Ma is the mass of a, Mc is the mass of c, La is the radius of a from point O, Lc is the radius of c from point O. Prove by simplest method that Equation E is wrong.
Answer 105 - Let Ma = 0 and Mc = 1 as assumption. Substitute them into Equation E as I = Ma x La x La + Mc x Lc x Lc = 0 + Lc x Lc = Lc x Lc. However, m = (0 x 1) / (0 + 1) = 0, then I = Lc x Lc, which is not equal to 0 but I = m x L x L = 0 x L x L = 0. Equation E is proven wrong. 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 NUMERICAL METHODS - EXAMPLE 19.2 : For a mixture of benzene (B), toluene (T) and xylene (X), the equation applies where x for B, T and X will sum up to 1. The equation of x for each component is x = (L / V + 1) (F) / (L / V + K). The data of F for each component are : 0.5 for B, 0.35 for T, 0.15 for X. The data of K for each component are : 1.98 for B, 0.76 for T, 0.24 for X. When x for B + x for T + x for X = 1, find the values of (a) L / V; (b) x for each component of B, T, X respectively. You may use Excel program - Data : What-If-Analysis for Goal Seek to perform the iterative calculations.
Question 27 – By using Excel or other easiest programming package, explain how I, the integral of sin x dx from 0 to 3.142 could be approximated using random number. Find the exact value of I.
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