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What is the wavenumber of the stretching vibrational mode for the CO molecule, given that the force constant of the bond is 680 N*m-1? Is this mode IR-active? (Hint: μ should be in kg)

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Answer:

1.10134 * 10⁻⁹m⁻¹

Explanation:

K = 680Nm⁻¹

μ = ?

μ = (m₁ + m₂) / m₁m₂

compound = CO

C = 12.0 g/mol = 0.012kg/mol

O = 16.0g/mol = 0.016kg/mol

μ = (m₁ + m₂) / m₁m₂

μ = (0.012 + 0.016) / (0.012*0.016) = 145.83

v = 1/2πc * √(k/μ)

ν = 1/ 2*3.142* 3.0*10⁸ * √(630/145.83)

v = 5.30*10⁻¹⁰ * 2.078

v = 1.10134*10⁻⁹m⁻¹

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