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Molar absorptivity, also known as the extinction coefficient, is a measure of how strongly a chemical species absorbs light at a given wavelength. It is denoted by the symbol \( \epsilon \) and has units of liters per mole per centimeter \( L/(mol \cdot cm) \). Molar absorptivity is an intrinsic property of the substance and can help identify or quantify the substance based on how much light it absorbs at a specific wavelength. In the provided exercise, compound Y has a molar absorptivity of 1000 L/(mol \cdot cm) at 390 nm, which means every mole of Y absorbs 1000 liters of light per centimeter of path length at that wavelength.

Light absorption is the process by which a substance captures and assimilates energy from light. This process follows the Beer-Lambert Law, which states that the amount of light absorbed by a substance is directly proportional to its concentration and the path length the light travels through. The formula representing this relationship is: \[ A = \epsilon l c \], where A is the absorbance (no units), \( \epsilon \) is the molar absorptivity, l is the path length (in cm), and c is the concentration (in mol/L). In our example, an unknown solution of compound Y has an absorbance of 0.750, indicating that the light's intensity has been significantly reduced while passing through the substance.

In the Beer-Lambert Law, concentration calculation involves rearranging the formula to solve for c. The formula is: \[ c = \frac{A}{\epsilon l} \]. Given the values from the exercise, absorbance A = 0.750, molar absorptivity \( \epsilon \) = 1000 L/(mol \( \cdot \) cm), and the path length l = 1 cm, we substitute these:

\[ c = \frac{0.750}{1000 \times 1} = 0.00075 \ mol/L \]. This calculation shows that the concentration of compound Y in the solution is 0.00075 mol/L.

Unit conversion is a crucial step in scientific calculations as it ensures consistency and understanding of data. Frequently, concentrations can be expressed in different units such as moles per liter (mol/L), millimoles per liter (mmol/L), or micromoles per liter (μmol/L). In our exercise, the calculated concentration is 0.00075 mol/L. To convert this into millimoles per liter, we multiply by 1000:\[ 0.00075 \ mol/L = 0.750 \ mmol/L \]. Hence, the solution concentration is 0.750 mmol/L, which matches option (e) in the problem statement. Always ensure units are consistent throughout your calculations to avoid errors.