Question

The C-C stretching vibration of ethylene can be treated as a harmonic oscillator.a. Calculate the ratio of the fundamental frequencies for ethylene and deuterated ethyleneb. Putting different substituents on the ethylene can make the C-C bond longer or shorter.For a shorter C-C bond, will the vibrational frequency increase or decrease relative toethylene? Why?c. If the fundamental vibrational frequency for the ethylene double bond is 2000 cm^-1,what is the wavelength in nm for the first harmonic vibration frequency?

Answer 1

The fundamental frequency of deuterated ethylene will be lower compared to ethylene due to its larger reduced mass. A shorter C-C bond in ethylene compared to a substituted ethylene will result in a higher vibrational frequency. The wavelength in nm for the first harmonic vibration frequency of ethylene can be calculated using the formula: wavelength = speed of light / frequency.

Step-by-step explanation:

The ratio of the fundamental frequencies for ethylene and deuterated ethylene can be calculated using the reduced mass formula, which takes into account the masses of the atoms involved in the vibration. Since deuterated ethylene has a greater mass due to the presence of deuterium (a heavier isotope of hydrogen), its reduced mass will be larger.

Therefore, the fundamental frequency of deuterated ethylene will be lower compared to ethylene.

When substituents are added to ethylene, they can affect the length of the C-C bond. For a shorter C-C bond, the vibrational frequency will increase relative to ethylene. This is because a shorter bond has higher bond strength, which corresponds to a higher vibrational frequency.

If the fundamental vibrational frequency for the ethylene double bond is 2000 cm⁻¹, the wavelength in nm for the first harmonic vibration frequency can be calculated using the formula: wavelength = speed of light / frequency. Converting the frequency to Hz (1 cm⁻¹ = 2.99792458 × 10¹⁰ Hz), the wavelength is approximately 149.896 nm.