To calculate the bond length between carbon and oxygen atoms in carbon monoxide CO , we can use Hooke's Law and the concept of reduced mass. Hooke's Law states that the force acting on a spring is proportional to the displacement from its equilibrium position:F = -k * xwhere F is the force, k is the force constant, and x is the displacement from the equilibrium position.The reduced mass of a diatomic molecule can be calculated using the formula: = m1 * m2 / m1 + m2 where m1 and m2 are the masses of the two atoms in the molecule. For carbon monoxide, m1 is the mass of carbon C and m2 is the mass of oxygen O . The atomic masses of carbon and oxygen are approximately 12 amu and 16 amu, respectively. To convert these atomic masses to kilograms, we can use the conversion factor 1 amu = 1.66054 10^-27 kg:m1 = 12 amu * 1.66054 10^-27 kg/amu = 1.99265 10^-26 kgm2 = 16 amu * 1.66054 10^-27 kg/amu = 2.65672 10^-26 kgNow, we can calculate the reduced mass: = 1.99265 10^-26 kg * 2.65672 10^-26 kg / 1.99265 10^-26 kg + 2.65672 10^-26 kg = 5.297 10^-53 kg^2 / 4.649 10^-26 kg = 1.139 10^-27 kgNext, we can use the force constant k and the reduced mass to calculate the vibrational frequency of the molecule using the formula: = 1 / 2 * k / where k is the force constant 1070 N/m and is the reduced mass 1.139 10^-27 kg : = 1 / 2 * 1070 N/m / 1.139 10^-27 kg = 1 / 2 * 9.396 10^26 s^-2 = 4.864 10^13 HzFinally, we can use the vibrational frequency to calculate the bond length r using the formula:r = c / 2 * where c is the speed of light 2.998 10^8 m/s and is the vibrational frequency:r = 2.998 10^8 m/s / 2 * 4.864 10^13 Hz r = 3.083 10^-11 mSo, the bond length between the carbon and oxygen atoms in carbon monoxide CO is approximately 3.083 10^-11 meters or 1.13 angstroms .