To calculate the bond length between a carbon and a hydrogen atom in methane, we can use the following equation:Bond length = sqrt 2 * Bond energy / Force constant * Avogadro's number First, we need to convert the bond energy from kcal/mol to J/mol:104.2 kcal/mol * 4184 J/kcal = 435888 J/molNow, we can plug in the values into the equation:Bond length = sqrt 2 * 435888 J/mol / 500 N/m * 6.022 x 10^23 mol^-1 Bond length = sqrt 871776 J/mol / 3.011 x 10^23 N Bond length = sqrt 2.896 x 10^-21 m^2 Bond length 1.70 x 10^-10 mSo, the bond length between a carbon and a hydrogen atom in methane is approximately 1.70 x 10^-10 meters or 1.70 angstroms .