To calculate the bond length between two oxygen atoms in an O2 molecule, we can use the Morse potential equation, which relates the bond energy, reduced mass, and bond length. The equation is:E = 1/2 * k * r - r0 ^2where E is the bond energy, k is the force constant, r is the bond length, and r0 is the equilibrium bond length.First, we need to convert the bond energy from kJ/mol to J/mol:E = 498 kJ/mol * 1000 J/1 kJ = 498000 J/molNext, we need to convert the reduced mass from g/mol to kg/mol: = 15.9994 g/mol * 1 kg/1000 g = 0.0159994 kg/molNow, we can use the harmonic oscillator approximation to relate the force constant, k, to the reduced mass, , and the vibrational frequency, :k = 2 ^2 * The vibrational frequency can be calculated using the bond energy and Planck's constant h : = E / hwhere h = 6.626 x 10^-34 Js = 498000 J/mol / 6.626 x 10^-34 Js = 7.515 x 10^12 HzNow, we can calculate the force constant, k:k = 2 * 7.515 x 10^12 Hz ^2 * 0.0159994 kg/mol = 4.784 x 10^3 N/mFinally, we can use the Morse potential equation to find the equilibrium bond length, r0. We can rearrange the equation to solve for r0:r0 = sqrt E / 1/2 * k r0 = sqrt 498000 J/mol / 1/2 * 4.784 x 10^3 N/m = 3.22 x 10^-10 mSo, the bond length between two oxygen atoms in an O2 molecule is approximately 3.22 x 10^-10 m or 322 pm.