(a) If a complex absorbs light at \(610 \mathrm{nm},\) what color would you expect the complex to be? (b) What is the energy in joules of a photon with a wavelength of \(610 \mathrm{nm}\) ? (c) What is the energy of this absorption in \(\mathrm{kJ} / \mathrm{mol} ?\)

**To determine the color we would expect the complex to be, we need to understand the color wheel and the complementary color theory. When a complex absorbs light at a specific wavelength (color), it reflects the complementary color, which is what we perceive as its color. The complementary colors are as follows: - Red (650-750 nm) ↔ Cyan - Green (495-570 nm) ↔ Magenta - Blue (450-495 nm) ↔ Yellow - Yellow (570-590 nm) ↔ Blue - Magenta (380-450 nm) ↔ Green - Cyan (500-520 nm) ↔ Red Since the complex absorbs light at 610 nm, which falls within the red wavelength range, its complementary color is cyan. So, the complex will appear cyan. **

**To calculate the energy of a photon with a wavelength of 610 nm, we will use the Planck's equation: \( E = hf \) where E is the energy, h is the Planck's constant (6.626 x 10^{-34} Js), and f is frequency. However, we are given the wavelength (λ), not frequency, so we need to use the speed of light equation: \(c = f\cdot \lambda\) where c is the speed of light (3.00 x 10^8 m/s) and λ is the wavelength. First, we need to convert the wavelength from nanometers to meters: \(610 \ \text{nm} = 610 \times 10^{-9} \ \text{m}\) Now, we calculate the frequency: \(f = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \ \text{m/s}}{610 \times 10^{-9} \ \text{m}} = 4.92 \times 10^{14} \ \text{Hz}\) Finally, use the Planck's equation to calculate the energy of a photon: \(E = (6.626 \times 10^{-34} \ \text{Js})\times(4.92 \times 10^{14}\ \text{Hz}) = 3.26 \times 10^{-19} \text{J}\) So, the energy of a photon with a wavelength of 610 nm is \(3.26 \times 10^{-19} \text{J}\). **

**To convert the energy to kilojoules per mole, we will use Avogadro's number (6.022 x 10^{23} mol^{-1}): \( E_{\text{mol}} = 3.26 \times 10^{-19} \text{J} \times \frac{6.022 \times 10^{23}\ \text{mol}^{-1}}{1\ \text{mol}} \times \frac{1\ \text{kJ}}{10^3 \text{J}} \) \(E_{\text{mol}} = 196.4\ \text{kJ/mol}\) So, the energy of this absorption in kilojoules per mole is 196.4 kJ/mol.