Question

Compute the interatomic distance between two atoms inside a diatomic molecule given spectroscopic data (the rotational temperature) $LaTeX: \Theta_{rot}$ Θ r o t

This problem has two questions. The first is for a real molecule . The second is a hypothetical molecule (made up atomic masses and $LaTeX: \Theta_{rot}$ Θ r o t )

1) compute the internuclear separation for ³⁵Cl₂ in picometers (pm). For consistent mass data use values from:

2) Consider a hypothetical diatomic molecule where the mass of atom 1 = 45.861 Daltons and the mass of atom 2 = 21.103 Daltons. If the rotational temperature $LaTeX: \Theta_{rot}=$ Θ r o t = 3 K, what is the internuclear distance in picometers.

Answer 1

DATE: PAGE NO 20 OR 2 Ke 2 h han h. Planck's constant Rotational Temporalu KB= Boltzman constant I Moment of Inertia (ur?) u Reduce mass r= Interatomic distance = 4x²x2 kg OR (6.626 X 10-34) 2 (Js) ² 4X3:14x 3.14 X 2 X 1:38 X10 JkX 10.35IK 1.149 X 10 -49 xq m ² P = M² u mixm2 = (58:06 x 10-27 kg) - mitm, 2x 58.06 x 10 u= 29.038 10.27 kg. rs I = 1:1498 10-40 kg m² u 29.03% 10-27 xq = 0.039 X 10-18 Jo.039x 10-18 1988 10-12 m = = 198pm

othelial dalam molecule 0 IE (6-626X10- Ux2 Ka I 4X3-14X3-14 Y 38 X 10 - JRX3 I - 0.1344 x 10-45 kg ma u= mim2 m +m = 95-86) X 21. 103 6.022 x 1026 bis 22 X10 (45.861 +21.103) 6.022 x 10 ls 45.861 x 21.103 x 10.26 6.022 = 2.399 X 10-26 Kg 2 I - 0.1344 X 10-45 kg 2.399x 10.26 kg 0.0 560 X 16-19 0.0790 X 109 m 79.8 X 10-12 m 29.8 pm