# The studying and calculation of the diatomic molecule CIF

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## The studying and calculation of the diatomic molecule CIF

Assignment 9

We are going to start by studying the diatomic molecule ClF in detail.

The masses of the isotopes involved are 35Cl = 34.96885269 g/mol, 37Cl = 36.96590258 g/mol, and 19F = 18.9984031629 g/mol. 35Cl is ~75% naturally abundant and 37Cl is ~25% naturally abundant.

1) a) Firstly, calculate the moment of inertia for 35Cl19F given the equilibrium ground state bond distance of 1.628313 angstroms.

b) Secondly, specify (by identifying the corresponding quantum numbers) which transitions are responsible for the 1st 4 lines of the rotational absorption spectrum

c) Thirdly, calculate the line frequencies of the first 4 lines of the 35Cl19F rotational spectrum.

d) Fourthly, calculate the corresponding line frequencies of the 37Cl19F diatomic molecule.

2) a) The vibrational frequency of the ground state for 35Cl19F is 786.15 cm-1. Calculate the force constant of the bond.

b) Assuming a similar force constant for 37Cl19F, what is its vibrational frequency?

c) If the dissociation energy for the ground state of 35Cl19F is 258078.39 cm-1, calculate the zero point energy on the same scale (Hint: zero energy is defined as the fully dissociated/separated atoms)

d) Calculate the anharmonicity constant for the ground state of 35Cl19F.

### Plot

3) a) Plot an anticipated Vib-Rot spectrum of ClF. Be sure to incorporate the following:

The line spacings and approximate relative intensities of both 35Cl19F and 37Cl19F.

Specify the x-axis and identify the P, Q, R branches. Be sure to specify each Q branch frequency.

Make note of which peaks are converging or diverging based on what you know so far.

b) What role does ‘nuclear statistics’ play in the plot above? Explain.

In addition to the ground state, 35Cl19F can also exist in an excited state that is 18826.4 cm-1 above the ground state. In the excited state, the vibrational spacings are 363.1 cm-1, the anharmonicity constant is 0.023795 and the rotational spacings are 0.3319 cm-1.

4) a) In an electronic-vib-rot spectrum of 35Cl19F, which branch exhibits a ‘branch head’? Calculate the value of J at which the branch head occurs.

b) Describe how the structure of the molecule changes in the excited state (Hint: what happened to the bond distance and force constant)

c) Plot an energy level diagram to scale for the ground and excited states of 35Cl19F (eg: see fig 13B.2 – but add rotational levels as well). Incorporate all the information you have available (rot & vib spacings, bond distances, potential well depths, etc).

d) Assuming the sample (35Cl19F) consists of a gas at 25 degrees C with molecules moving at 400m/s, what is the minimum linewidth you’d expect in an experimental spectrum for the

i) ground state v=0 -> ground state v=1 transition

ii) ground state v=4 -> excited state v=4 transition

e) Consider the possibility that the excited state v=4 is a pre-dissociative state (only the v=4 state and no others). What will happen to the linewidth of the second transition above? How does this affect the overall experimental spectrum. Explain

### The studying and calculation of the diatomic molecule CIF

f) For the ground state v=4 -> excited state v=4 transition to occur, what must be true about their wavefunctions? Explain.

g) For the ground state v=0 -> ground state v=1 transition to be observed spectroscopically, what must be true about the molecular change during the transition? Explain.

h) Which form of emission (stimulated or spontaneous) dominates for each of these two transitions (calculate relative rates for each)?

i) Briefly plot a Vib-Rot Raman spectrum of the ground electronic state of 35Cl19F incorporating the laser frequency v0 and other information you know (from above).

5) Calculate the number of normal modes for NH4. Identify if the molecule exhibits an IR absorbtion spectra or a Raman spectrum and draw one specific absorbtion mode (if any are active) and one specific Raman mode (if any are active).

6) A Dubosq colorimeter consists of a cell of fixed path length and a cell of variable path length. By adjusting the length of the latter until the transmission through the two cells is the same, the concentration of the second solution can be inferred from that of the former. Suppose that a plant dye of concentration 40 μg/dm3 is added to the fixed cell, the length of which is 1.80 cm. Then a solution of the same dye, but of unknown concentration, is added to the second cell. It is found that the same transmittance is obtained when the length of the second cell is adjusted to 1.18 cm. What is the concentration of the second solution?

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