Question

1. The rotational vibra R branch. P branch A B C DEF 2700 -1 2600 2500 2400 V/cm Each line in this spectrum corresponds to a transition from a state with n 0 and J Jinitial to a state with n- 1 and J Jfinal. of this a. What are the allowed values ofAJ Je Jinitial in the P and R branches, respectively, final spectrum? b. What are the values of Jinitial and Janal for lines A, B, C, D, E, and F in this spectrum? 3-2 c. In the harmonic oscillator rigid rotor approximation, the rotational-vibrational energy ofa diatomic molecule is given by J 0, 1, 2 where v and B In units of wave numbers, this becomes heart r slow fast BJ (J+1) n vvib hc r lines A, B, C, D, E, and sing the latter equation, derive expressions for the wave numbers v and the rotational constant F in terms of the pure vibrational wave number (2nc) Vk /H 2hcl

Anyone plz answer these questions? Especially c) read the questions carefully and answer fully not only wavenumbers but also F and rotational constant

Answer 1

a) The allowed values of delta J = J_f - J_i in the P & R prances of the spectrum is delta J = pm 1[therefore From selection rule for vibration at rotational spectra] b. The above given figure in the problem is remodified in general spectrum. The initial and final values of J for A/ delta J Rightarrow 3 rightarrow 2 B/ delta J Rightarrow 2 rightarrow 1 C/ delta J Rightarrow 1 rightarrow 0 A/ delta J Rightarrow 0 rightarrow 1 E/ delta J Rightarrow 1 rightarrow 2 F/ delta J Rightarrow 2 rightarrow 3 c. from the Given data times in terms of wave number is bar{E_n, j} = E_n.J/hc = (n + 1/2) bar{r_vib} + bar{B} J(J + 1) Expressions of wave numbers for different lines are A, AJ Rightarrow 3 rightarrow 2 Rightarrow J = 3, n = 2 bar{E_n, J} = (5/2) bar{v_vib + bar{B}(12) = (5.2) bar{V_vib + 12 bar{B} B, AJ Rightarrow 2 rightarrow 1 Rightarrow J = 2, n = 1 bar{E_n, J} = (3/2) bar{v_vib + 6 bar{B} C, AJ Rightarrow 1 rightarrow 0 Rightarrow J = 1, n = 0 bar{E_n, J} = (1/2) bar{v_vib + 2 bar{B} D, AJ Rightarrow 0 rightarrow 1 Rightarrow J = 0, n = 1 bar{E_n, J} = (3/2) bar{v_vib} E, AJ Rightarrow 1 rightarrow 2 Rightarrow J = 1, n = 2 bar{E_n, J} = (5/2) bar{v_vib + 2 bar{B} F, AJ Rightarrow 2 rightarrow 3 Rightarrow J = 2, n = 3 bar{E_n, J} = (7/2) bar{v_vib + 6 bar{B}