Unleashing Light: Calculating the Maximum Wavelength for O2 Molecule Dissociation

To solve this problem, we'll use Einstein's photoelectric effect equation, which says energy of a photon (E) is equal to Planck's constant (h) times the speed of light (c) divided by the wavelength (λ). Here's the formula: E = h * c / λ We're trying to find the wavelength, so we need to rearrange the equation to solve for λ: λ = h * c / E The given bond dissociation energy of O2 is 598.7 kJ/mol. We need to convert this to joules per molecule because Planck's constant has units of joules-seconds. To do this, the bond disassociation energy should be divided by Avogadro's number (approximately 6.022 x 10^23 molecules/mol): E = 598.7 kJ/mol / (6.022 x 10^23 molecules/mol) * (1000 J/1 kJ) = 9.94*10^-19 J/molecule Now you can substitute the given Planck's constant (6.626*10^-34 J.s), speed of light (3.0*10^8 m/s), and calculated energy into the equation: λ = 6.626*10^-34 J.s * 3.0*10^8 m/s / 9.94*10^-19 J/molecule After calculating the above, λ=2.00*10^-6 m. However, the problem asked for the wavelength in nanometers, not meters. We can convert meters to nanometers by remembering that 1 m = 10^9 nm: λ = 2.00*10^-6 m * (10^9 nm/m) = 2000 nm Therefore, the maximum wavelength of a photon that can cause the dissociation of an O2 molecule is about 2000 nm.