Question

03 (5 points) Consider the vibrational spectra of the Co diatomic molecule in its ground electronic state. If the fundamental frequency of CO is 6.5x1054 1. Determine the force constant k? (MW: C = 12,0 = 16) (2 points) 2. Determine the AE between the first two vibrational levels (3 points) Show your work and make sure to include chapter level explanations

Answer 1

PAGE: DATE Answer Given, the fundo mental Frequency of co is 3 6. 5 *lo 2 Mole cular weight oF Molecuuar weight of C Force cons tant calcuuate we have to For Calcuwating iU's calculote Force cons tant first we reduced mass red uced mass Step cauculate To OF Co The reduced mass OF cal cwated Can be CO mc mo 12 xG 23 G. 857 9/mol O Kg /mo o. o o 8 67 Kg/mol 023 23 .1384 1026 Kg

PAGE: DATE: Step To calcwate Force constont The force constant 'K' can be calculated as K 19 2 T squaring on both side, L4n202 K 4 x C3.14) x (6.5 x103) x ( t.i384 xI626) K 1896. 88 Kg /s Step CT calcuuate A E between the First two vibrational levels Khow that, We En- hs For pir st vibrational |evel energy is,

PAGE DATE similarly Por 2nd vibratio nal evel s, E2 E AF _b७ E -34 G. 626 lO Here, J.S 34 K 6. 5 x 1o 13 AE 2 6, 626 4-306 X1020J 4-306 I6* 20
1 Force constant 'k' is 1896.88 N/m

2. ∆E for the first two vibrational levels is 4.306 * 10^-20 J