To calculate the bond length between two hydrogen atoms, we can use the Morse potential equation, which relates bond energy, bond length, and the equilibrium bond length. The Morse potential equation is:V r = D_e * 1 - exp -a * r - r_e ^2where:V r is the potential energy as a function of the bond length r,D_e is the bond energy in this case, 436 kJ/mol ,a is the Morse potential parameter,r is the bond length,r_e is the equilibrium bond length.However, we do not have enough information to directly calculate the bond length using the Morse potential equation. Instead, we can use the empirical relationship between bond energy and bond length, which is derived from experimental data.For diatomic molecules like H2, the bond energy E and bond length r are related by the following equation:E = k / r^nwhere k and n are constants that depend on the specific molecule.For the H2 molecule, the constants k and n have been determined experimentally to be:k = 2.65 10^5 kJ/mol^nn = 2.5Now, we can solve for the bond length r using the given bond energy E = 436 kJ/mol :436 kJ/mol = 2.65 10^5 kJ/mol^2.5 / r^2.5Rearranging the equation to solve for r:r^2.5 = 2.65 10^5 kJ/mol^2.5 / 436 kJ/molr^2.5 607.34 ^2.5Now, we can take the 2.5th root of both sides to find r:r 607.34^1/2.5 r 0.741 So, the bond length between two hydrogen atoms in an H2 molecule is approximately 0.741 74.1 pm .