To calculate the bond length between two hydrogen atoms H-H bonded together by a single covalent bond, we can use the formula for the potential energy of a diatomic molecule:V r = 1/2 * k * r - r0 ^2where V r is the potential energy, k is the force constant, r is the bond length, and r0 is the equilibrium bond length.We can find the equilibrium bond length r0 by finding the minimum of the potential energy function. To do this, we can take the derivative of the potential energy function with respect to r and set it equal to zero:dV r /dr = k * r - r0 = 0Solving for r0, we get:r0 = rNow, we can use the bond energy to find the potential energy at the equilibrium bond length:V r0 = Bond energy = 436 kJ/molSince 1 J = 1 Nm, we can convert the bond energy to joules:V r0 = 436 kJ/mol * 1000 J/1 kJ * 1 mol/6.022 x 10^23 molecules 7.24 x 10^-19 J/moleculeNow, we can plug this value into the potential energy formula:7.24 x 10^-19 J/molecule = 1/2 * 432 N/m * r0 - r0 ^2Since r0 - r0 ^2 = 0, the equation simplifies to:7.24 x 10^-19 J/molecule = 1/2 * 432 N/m * r0^2Now, we can solve for r0:r0^2 = 7.24 x 10^-19 J/molecule / 1/2 * 432 N/m r0^2 3.35 x 10^-19 m^2Taking the square root of both sides:r0 1.83 x 10^-10 mSo, the bond length between two hydrogen atoms H-H bonded together by a single covalent bond is approximately 1.83 x 10^-10 meters or 0.183 nanometers.