To calculate the bond length between a hydrogen atom and an oxygen atom in an H2O 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 Joules:463 kJ/mol * 1000 J/1 kJ * 1 mol/6.022 x 10^23 molecules = 7.684 x 10^-19 JNext, we can calculate the force constant k using the reduced mass and the vibrational frequency :k = * 2 * * ^2The vibrational frequency can be calculated using the bond energy E and the reduced mass : = 1/ 2 * * sqrt k/ We can rearrange the equation to solve for k:k = * 2 * * ^2Since we know the bond energy E and the reduced mass , we can substitute the values into the equation:7.684 x 10^-19 J = 1/2 * k * r - r0 ^2Now, we need to find the equilibrium bond length r0 . The equilibrium bond length can be found using the Morse potential equation:r0 = r - sqrt 2 * E / k We can rearrange the equation to solve for r0:r0 = r - sqrt 2 * 7.684 x 10^-19 J / k Now, we can substitute the values of E and into the equation:r0 = r - sqrt 2 * 7.684 x 10^-19 J / 1.6735 x 10^-27 kg * 2 * * ^2 Unfortunately, we do not have enough information to solve for the vibrational frequency and the bond length r . However, we can use experimental data to find the bond length. The bond length between a hydrogen atom and an oxygen atom in an H2O molecule is approximately 0.96 angstroms or 9.6 x 10^-11 m.