a) This question requires use of the equation that relates the relative populations of states to the temperature and the energy difference between them;
\n\\[\\frac{N_u}{N_l}=e^{\\frac{-{\\Delta}E}{kT}}\\]
\n\\[\\frac{N_u}{N_l}=e^{\\frac{-{\\var{Energy_mantissa}\\times10^\\var{Energy_log}}}{1.38~\\times~10^{-23}~\\times~\\var{temp}}}=\\var{D}\\]
\n\nb) To convert the energy of a photon into a frequency;
\n\\[E=h\\nu~\\]
\nso
\n\\[\\frac{E}{h}=\\nu=\\frac{\\var{Energy_mantissa}~\\times~10^\\var{Energy_log}~\\rm J}{6.626~\\times10^{-34}~\\rm~J~s}=\\var{Freq_mantissa}\\times10^{\\var{Freq_log}}~{\\rm Hz}\\]
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\n$N_u/N_l$ = [[0]]
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\n[[0]] $\\times$ 10[[1]] Hz
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