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Homework 22 (Not Due)

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    In a 5.0 mM solution, a solute absorbs 90% of a visible light as the beam passes through a 80 mm cell. Calculate the molar absorptivity of this solute.


    Find the uncertainty of simultaneously measuring the frequency and wavelength of an emission, if the wavelength is 430 nm and the excited state lifetime is 0.50 nanoseconds.


    Outline three relaxation processes that occur in a molecule after photoexcitation of a valence electron to a higher lying molecular orbital. What is the end result of the relaxation (e.g., in what state is the molecule after photoexcitation)?


    One of the excited states of a \(C_2\) diatomic molecule has the electron configuration (i.e., a \(\sigma^* \rightarrow \sigma\) transition):

    \[(σ_{1s})^2(σ_{1s}^*)^2(σ_{2s})^2(σ_{2s}^*)^1(π_{2p_x})^2 (π_{2p_y})^2(σ_{2p})^1\]

    1. What is the bond order of \(C_2\) in this excited state?
    2. What is the bond order of \(C_2\) in the ground state (assume aufbau principle is fully applicable)?
    3. How does the bond length in this excited state compare to that in the ground state?
    4. How does the bond energy in this excited state compare to that in the ground state?
    5. Is the excited state paramagnetic or diamagnetic?
    6. Is the ground state paramagnetic or diamagnetic?
    7. To technically answer questions 5. you need to know another piece of information: What is it?

    Q22.5 Advanced Question

    However, the experimental fact is that \(C_2\) has a triplet ground state, so two electrons must be unpaired (and with same orientation). We explain this by noting that the \(\pi_{2p_x}\), \(\pi_{2p_y}\), and \(\sigma_{2p_z}\) molecular orbitals are quite close in energy. There is a concept called spin pairing energy, used in crystal field theory, that argues it takes energy to pair the electrons within an orbital. In \(C_2\) this spin pairing energy is greater than the difference in \(\pi\) and \(\sigma\) MOs, so that one electron is placed in the slightly higher orbital. Draw the true molecular orbital diagram for \(C_2\)? What is is the bond order for this molecular orbital model?


    What is the relative relationship between the timescale for internal conversion, intersystem crossing and emission for a chromophore to be a good fluorophore (i.e., likes to emit photons after excitation)?

    Homework 22 (Not Due) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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