upper state P(J+1) R(J-1) J+1 lower state J - 1 Ignoring centrifugal distortion effects, use the expressions for the energies of the J-1 and J+1 levels of the lower state (which are B"(J-1) and B"(J+1)(J+2), respectively) to derive: R(J-1) - P(J+1) - B"(4J+2), where B" is the rotational constant of the lower state. (f). Plot R(J-1) - P(J+1) vs. (4J + 2) for the listed line positions and your assignments of the lines. If your plot is not extremely close to a straight line, your assignment of the rotational lines is incorrect. Perform a linear least-squares fit to extract the slope of the line, which gives the value of B" for the v"-0 ground vibrational level of the ground electronic state of "Ni -C. (g). Similarly, one may consider transitions originating from the same lower state level, but which terminate on different upper state levels (such as R(J) and P(J)). The difference in these frequencies then only depends on the spectroscopic constants of the excited state. Ignoring centrifugal distortion effects, apply this strategy to derive R(J) - P(J) - B' (4J+2), where B' is the rotational constant of the upper state. (h). Plot R(J) - P(J) vs. (4J + 2) for your assignment of the lines. As in part (f), your plot should be extremely close to a straight line. Perform a linear least-squares fit to extract the slope of the line, which gives the value of B' for the excited electronic state of Ni -C. (i). Finally, evaluate the bond length, Ro, of NiC from the relationship Bo(em") - 16.8576313/[u(amu)Ri (A)] This expression relates the rotational constant, Bo, in cm" units to the reduced mass, u, in atomic mass units and to the bond length, Ro, in A units. The subscripts "0" refer to the fact that these constants pertain to the v 0 level. In general, B, is the expectation value of this quantity for the v vibrational level: By = J Vu (R ) 16.8576313 1.(R)dR . AL R2 Page 7 of 9