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Determine whether the following transitions are allowed or forbidden: a. \(\sqrt[3]{\Pi}_{u} \rightarrow^{3} \Sigma_{g}^{-}\) \(\mathbf{b} .^{1} \Sigma_{g}^{+} \rightarrow^{1} \Pi_{g}\) \(\mathbf{c} .^{3} \Sigma_{g}^{-} \rightarrow^{3} \Pi_{g}\) d. \(^{1} \Pi_{g} \rightarrow^{1} \Delta_{u}\)

Ozone \(\left(\mathrm{O}_{3}\right)\) has an absorptivity at \(300 .\) nm of 0.00500 torr \(^{-1} \mathrm{cm}^{-1} .\) In atmospheric chemistry the amount of ozone in the atmosphere is quantified using the Dobson unit (DU), where 1 DU is equivalent to a \(10^{-2} \mathrm{mm}\) thick layer of ozone at 1 atm and \(273.15 \mathrm{K}\) a. Calculate the absorbance of the ozone layer at \(300 .\) nm for a typical coverage of \(300 .\) DU. b. Seasonal stratospheric ozone depletion results in a decrease in ozone coverage to values as low as \(120 .\) DU. Calculate the absorbance of the ozone layer at this reduced coverage. In each part, also calculate the transmission from the absorbance using Beer's Law.

Green fluorescent protein (GFP) and variants of this protein have been developed for in vivo FRET studies (Pollok B. and Heim R. Trends in Cell Biology \(9(1999): 57\) ). Two variants of GFP, cyan fluorescent protein (CFP) and yellow fluorescent protein (YFP), form a FRET pair where \(R_{0}=4.72 \mathrm{nm} .\) The excited-state lifetime of the CFP donor in the absence of YFP is 2.7 ns. a. At what distance will the rate of energy transfer be equal to the excited- state decay rate for isolated CFP, equal to the inverse of the excited-state lifetime? b. Determine the distance at which the energy transfer rate will be five times the excited-state decay rate.