# Homework 11

- Page ID
- 204091

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q1

The rotational constant of \(H^{35}Cl\) is \(10.5909\; cm^{-1}\). Calculate the rotational constants of \(H^{37}Cl\) and \(^2H^{35}Cl\).

## Q2

Without calculating the specific values, arrange the following molecules in order of increasing value of their rotational constants, \(\tilde{B}\):

\(HF\), \(DF\), \(\ce{H–C#C–C#C–C#N}\), \(HD\), \(^{12}C^{16}O\), \(^{13}C^{16}O\), \(^{12}C^{18}O\), and \(CICN\)

## Q3

Given that the CO bond length in the molecule OCS is 0.1165 nm and the CS bond length is 0.1558 nm, determine its moment of inertia. At which frequencies (units Hz or GHz) do the \(J= 1 \rightarrow 0\) and \(2 \rightarrow 1\) transitions occur in the rotational spectrum of OCS?

## Q4

The rotational terms of a diatomic molecule (the energy levels expressed as wavenumbers) are given to a good approximation by this formula:

\[F_J = \tilde{B} J(J+1) - \tilde{D}J^2(J+1)^2\]

- Explain the meaning of \(J\), \(\tilde{B}\) and \(\tilde{D}\) in this expression.
- What selection rules apply to pure rotational spectroscopy?
- Derive an expression for the energy of transitions observed in a high resolution rotational spectrum.
- In a high resolution microwave study of \(^2H^{19}F\), the first four lines in the spectrum were observed at:

- 22.0180 cm
^{-1} - 44.0218 cm
^{-1} - 65.9970 cm
^{-1} - 87.9295 cm
^{-1}

- Deduce the values of \(\tilde{B}\) and \(\tilde{D}\) for \(^{2}H^{19}F\) (you can do this graphically, if you like).
- Determine the \(^2H^{19}F\) bond length from the above information.

## Q5

The molecule \(H^{35}Cl\) exhibits rotational absorption lines in the far infrared at the following wavenumbers (in cm^{-1}): 83.32, 104.13, 124.73, 145.37, 165.89, 186.23, 206.6, 226.86. (Note that there may be other lines in the microwave region, too.)

- Identify the transitions and determine the rotational and centrifugal distortion constants. Calculate the bond length of HCl.
- Predict the rotational constants for DCl.
- Did you use the rigid rotor or non-rigid rotor approximation for the above questions?

## Q6

What is the ground state electron configuration of Ne_{2 }molecule? Is this molecule stable? Promote one electron from the highest filled MO (HOMO) to the lowest unfilled MO (LUMO). The new configuration corresponds to an excited molecular state. Is the excited molecule stable? Draw (qualitatively) the potential curves of the Ne_{2} ground and excited states. Assume that two Ne atoms undergo collisions which can result in both ground and excited state molecules and consider the electromagnetic transitions occurring between these two states.