Concept explainers
(a)
Interpretation:
The vibrational frequency of the molecule has to be calculated.
Concept Introduction:
The energies are quantized in harmonic oscillator and are generally expressed as follows,
The force constant,
The vibrational quantum number is used to denote the energy levels of harmonic oscillator.
(a)
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Explanation of Solution
Given:
The m is replaced by the effective mass
The vibrational frequency, of the molecule is calculated as follows by the given m value into equation 1 as follows,
(b)
Interpretation:
The vibrational wavenumber of the given molecule has to be calculated.
Concept Introduction:
The energies are quantized in harmonic oscillator and are generally expressed as follows,
The force constant,
The vibrational quantum number is used to denote the energy levels of harmonic oscillator.
The vibrational wavenumber is determined by taking reciprocal of wavelength.
(b)
![Check Mark](/static/check-mark.png)
Explanation of Solution
The vibrational wavenumber for given molecule is determined as shown below,
(c)
Interpretation:
The vibrational wavenumber of the given molecules has to be calculated.
Concept Introduction:
The energies are quantized in harmonic oscillator and are generally expressed as follows,
The force constant,
The vibrational quantum number is used to denote the energy levels of harmonic oscillator.
The vibrational wavenumber is determined by taking reciprocal of wavelength.
(c)
![Check Mark](/static/check-mark.png)
Explanation of Solution
First, the
The vibrational frequency, of the molecule is calculated as follows by the given m value into equation 1 as follows,
The vibrational wavenumber for given molecule is determined as shown below,
Next, the
The vibrational frequency, of the molecule is calculated as follows by the given m value into equation 1 as follows,
The vibrational wavenumber is identified by considering that the given isotopic CO molecules are differ only in reduced masses since they have similar identical force constants. The frequency and wavenumber are inversely proportional to
Similarly, the
Similarly, the
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