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Answer:
Explanation:
From the given information:
At wavelength = 270 nm
[tex]\varepsilon x_1 = 1600 \ m^{-1} \ cm^{-1} \\ \\ \varepsilon y_1 = 200 \ m^{-1} \ cm^{-1}[/tex]
At 270 nm
Suppose x is said to be the solution for the concentration of x and y to be the solution for the concentration of y;
Then:
[tex]\varepsilon x_1 \ l + \varepsilon y_1 \ l= 0.5 \\ \\ A = A_1 + A_2[/tex]
[tex]1600 xl + 200 yl= 0.5[/tex]
Divide both sides by 200
[tex]8xl + yl = \dfrac{0.5}{200}[/tex]
[tex]8x + y = \dfrac{0.5}{200}l[/tex]
Use l = 1cm (i.e the standard length)
Then;
[tex]8x + y = \dfrac{0.5}{200} ---- (1)[/tex]
For 540 nm:
[tex]\varepsilon x_2 x \ l + \varepsilon y_2 y \ l= 0.5 \\ \\ 40 xl + 800 yl = 0.5[/tex]
[tex]x + 20 y = \dfrac{0.5}{400 \ l}[/tex]
since l = 1
[tex]x + 20 y = \dfrac{0.5}{400 \ } --- (2)[/tex]
Equating both (1) and (2) together, we have:
[tex]8x + y - 8x - 160 y = \dfrac{0.5}{200} - \dfrac{0.5 \times 8}{400} \\ \\ \implies - 159 y = \dfrac{0.5}{200} ( 1 - \dfrac{8}{2}) \\ \\ -159 y = \dfrac{-0.5 \times 3}{200} \\ \\ 159 \ y = 0.0075 \\ \\ y = \dfrac{0.0075}{159} \\ \\ y = 0.00004716 \\ \\ y = 4.7 \times 10^{-5 } \ M[/tex]