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Calculate the bond length between a carbon (C) and an oxygen (O) atom in carbon monoxide (CO), given that the bond energy is 1070 kJ/mol and the force constant is 1070 N/m.

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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 .

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