Final answer:
The wavelength of the photon that has just enough energy to break the bond in oxygen is approximately 399 nm.
Step-by-step explanation:
The bond energy of O2 is the energy required to break the O-O bond in oxygen. The bond energy for O2 is 498 kJ/mol. In order for a photon to break the bond in oxygen, it must have enough energy to overcome the bond energy. The energy of a photon is inversely proportional to its wavelength, so we can use the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3.00 x 108 m/s), and λ is the wavelength of the photon.
First, let's convert the bond energy from kJ/mol to J/molecule by multiplying by 1000:
498 kJ/mol x (1000 J/1 kJ) = 498,000 J/mol
Now, let's use the equation E = hc/λ to solve for the wavelength:
498,000 J/mol = (6.626 x 10-34 J·s)(3.00 x 108 m/s)/λ
Solving for λ:
λ = (6.626 x 10-34 J·s)(3.00 x 108 m/s) / 498,000 J/mol
λ = 3.99 x 10-7 m
Therefore, the wavelength of the photon that has just enough energy to break the bond in oxygen is approximately 399 nm.