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One of the most widely used applications of spectroscopy is for the quantitative determination of the concentration of biological molecules in solution. The absorbance of a solution, Ai, at wavelength i, is given by the sum of the product of e(k), the extinction coefficient/length of all components k (from 1 to N) obtained at the same wavelength and the concentrations of the components of the solution, C(k) (Yinoco et al., 2002). Consider a hypothetic experiment when a protein solution with four amino acids, M, N, O, and P, was measured using four different wavelengths, and the absorbance values were recorded. The extinction coefficients for the four amino acids for the four wavelengths are tabulated below. Estimate the concentration of the four amino acids in M. Compare your answers and the efficiency of solution using the Gauss Jordan method and the iterative Jacobi method. Wavelength eM (M-I) ~N (M-l) eO (M-l) ee (M-l) Ai 240 11300 8150 4500 4000 0.6320 250 5000 7500 3650 4200 0.5345 260 1900 3900 3000 4800 0.3310 280 1500 1400 2000 4850 0.1960
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