If 310 kJ/mol of energy is required to make the reaction proceed, what wavelength of light is necessary to provide this energy?

• A. 650 nm
• B. 750 nm
• C. 387 nm
• D. 500 nm

Answer: (C)

Verified step by step guidance

1. First, understand that the energy required for the reaction is given as 310 kJ/mol. This energy needs to be converted into energy per photon using Avogadro's number (6.022 x 10^23 mol^-1).
2. Convert the energy from kJ/mol to J/photon. Use the conversion factor: 1 kJ = 1000 J. So, 310 kJ/mol = 310,000 J/mol. Then, divide by Avogadro's number to find the energy per photon: E_photon = (310,000 J/mol) / (6.022 x 10^23 mol^-1).
3. Use the energy of a photon equation, E = h * c / λ, where E is the energy per photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters.
4. Rearrange the equation to solve for the wavelength, λ: λ = h * c / E_photon. Substitute the values for h, c, and the calculated E_photon into the equation.
5. Convert the wavelength from meters to nanometers by multiplying by 10^9, since 1 m = 10^9 nm. This will give you the wavelength of light necessary to provide the required energy.