Question

Atkins' Physical C... PZE.4 The force constant for the bond in CO is 1857 Nm . Calculate the vibrational frequencies (in Hz) of 'C', 'C', C'80, and 'C'80. Use integer relative atomic masses for this estimate. harmonic the integra and then u 0. (b) Calc section). (c 297 P7E.5 In infrared spectroscopy it is common to observe a transition from the v=0 to v= 1 vibrational level. If this transition is modelled as a harmonic oscillator, the energy of the photon involved is ħo, where w is the vibrational frequency. (a) Show that the wavenumber of the radiation corresponding to photons of this energy, V, is given by v=o/2nc, where c is the speed of light. (b) The vibrational frequency of 'H*Cl is w = 5.63 x 10'45-'; calculate ſ. (c) Derive an expression for the force constant ke in terms of v. (d) For Co the v= 0 + 1 transition is observed at 2170 cm ?. Calculate the force constant and estimate the wavenumber at which the corresponding absorption occurs for 14 CO. Use integer relative atomic masses for this estimate. P7E.11 The is most eas will find it operator w Table 7E.1. it can be re frequency Î=-1 The expect wavefunct PZE.6 Before attempting these calculations, see Problem P7E.5. The following data give the wavenumbers (wavenumbers in cm) of the v = 01 transition of a number of diatomic molecules. Calculate the force constants of the bonds and arrange them in order of increasing stiffness. Use integer relative atomic masses. (T), =- H5C1 HBr 1H127 12C160 147160 where N,, i 71 7 (thot

Answer 1

Solution P7 E.4 in co(Nm) Viblolion frequently VI VEL 20cu Whece, kis force constant for the bond u is the reduced mass in kg c = 3x108 mils speed of light ka 1957 Nm' lil (216 30006857 kg U=12x6 4957 9 12:16 v= t 1857 2x(3x108) JO1006857 1 = 2 :59x10 e HZ Lii , c3 10 7.172 9m = 0.007172 kg US 13x6 = 13+16 V = 1 [1857 27(3X108) / 00007172 V = 26-97x10-6 Hz) (iii) 22 18 u 12x18 12+ 18 7.2 m -0.007200 kg v= 1 T 1857 2.7(3x1080.0072 J = 26091810-8 H2 053X3 = 13x12 3+18 = 7.548gm = 0.007548kg. v=11857 27C 0.007548 v = 26.30X108 HZ