A pure rotational spectrum of a ${?}^{12}{C}^{16}O$ dimer molecule has been measured at some temperature $T.$ The picture below shows the plot of intensity $($in normed, but arbitrary units$)$ versus wave number; the spectrum of ${?}^{12}{C}^{16}O$ refers to the lines with higher intensity $($blue dots, if visible$).$ In addition, researchers did an isotope exchange for carbon and recorded a second pure rotational spectrum for the dimer ${?}^A{C}^{16}O($lines with lower intensity; red dots, if visible$).$ Unfortunately, the exact isotope mass is lost $-$ but then the two spectra are given. Use them to

a$.[2]$ Calculate the temperature in the experimental chamber.

b$.[2]$ Identify the carbon isotope used for $C$ exchange.

You can easily do the analysis even without a ruler and still do this to better than $3\%$ error. Furthermore, do the analysis for multiple lines and then average your result $($you may even catch serious mistakes that way$).$

wave number $c{m}^{-1}$