To solve this problem, we need a calibration curve of the absorption versus concentration of the copper salt at a given light frequency (Beer's law plot). If you have one, it's best to use the data from it.
According to the Lambert's Beer law:
A = Cl,
A - absorbance
l - the path length
ϵ - the molar absorptivity
Herefrom, С = A / ϵl
ϵl also call slope of the Beer's law plot, this value is a constant for each solution, you have to take it from your plot. Let's accept slope of the Beer's law plot = 432 L/mol.
Cresulting solution = 0.42/432 = 0.000972 mol/L
As our solution is diluted, we calculate the concentration of the original solution:
Cinitial solution = Сresulting solution*Vresulting solution/Vinitial solution = 0.000972*500/10 = 0.0486 mol/L
(Do not forget that we diluted 10 ml of the initial solution!)
Now we can find the mass of copper in the original solution:
m(Cu) = Cinitial solution*Vinitial solution*M(Cu) = 0.0486*0.1*64.55 = 0.309 g
Percent copper in the sample is:
(Cu) = 100%* m(Cu)/m(copper ore) = 100% * 0.309/2.2 = 14..04%.
Answer: initial molarity of the 100mL solution is 0.0486 mol/L and percent copper in the sample is 14.04%.