Complete the exercises below. a. A complex absorbs photons with an energy of 4.51 x 10⁻¹⁹ J. What is the wavelength of these photons? b. If this is the only place in the visible spectrum where the complex absorbs light, what color would you expect the complex to be?

Verified step by step guidance

1. Step 1: Use the equation that relates energy and wavelength of a photon: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J s} \), \( c \) is the speed of light \( 3.00 \times 10^8 \text{ m/s} \), and \( \lambda \) is the wavelength.
2. Step 2: Rearrange the equation to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).
3. Step 3: Substitute the given energy \( E = 4.51 \times 10^{-19} \text{ J} \), Planck's constant \( h = 6.626 \times 10^{-34} \text{ J s} \), and the speed of light \( c = 3.00 \times 10^8 \text{ m/s} \) into the equation to calculate \( \lambda \).
4. Step 4: Convert the calculated wavelength from meters to nanometers by multiplying by \( 1 \times 10^9 \text{ nm/m} \) to find the wavelength in the visible spectrum.
5. Step 5: Determine the color of the complex by identifying the complementary color of the absorbed wavelength. Use a color wheel or chart to find the color opposite to the absorbed wavelength in the visible spectrum.