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The following are sets of rotational quantum numbers
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(c)
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Chapter 14 Solutions
Physical Chemistry
- The following are sets of rotational quantum numbers (J,MJ,K). Label each indicated transition as either allowed or forbidden. Hint: Remember the rules for allowed values of the various quantum numbers. a (5,4,0)(3,6,0)b (8,2,2)(9,2,2) c (7,4,2)(7,4,2)d (4,2,5)(3,2,5)arrow_forwardWhat is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?arrow_forwardRotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?arrow_forward
- 3 The rotation motion of HCl molecules can be analyzed by treating each molecule as a rigid rotational constant B= 2.07x10^-22 Joules. a) what frequency of radiation will excite the transition from the J=1 energy level to the J=2 level in this case? b) what is the relative probability of observing an HCl molecule at the J=2 energy level, as compared to teh J=1 level, at 25.00 degrees C?arrow_forwardThe vibrational frequency of the hydrogen chloride HCl diatomic molecule is 8.97 x 1013Hz. chloride atom is 35.5 times more massive than hydrogen atom. (mµ = 1.67 x 0-27kg,c = 3.0 x 10°m/s) a) What is the force constant of the molecular bond between the hydrogen and the chloride atoms? b) What is the energy of the emitted photon when this molecule makes a transition between adjacent vibrational energy levels? c) What is the wavelength of the emitted photon? d) The possible wavelengths of photons emitted with the HCl molecule decays from the 2nd excited state eventually to the ground state(0 state).arrow_forwardUse the Tanabe-Sugano diagram to indicate the electronic transitions for the configurations below, i.e. for example, 'A2 →³T2 is one transition for ³F. (a) d³ (b) dºarrow_forward
- An H2 molecule is in its vibrational and rotational ground states. It absorbs a photon of wavelength 2.211 2 μm and makes a transition to the υ = 1, J = 1 energy level. It then drops to the υ = 0, J = 2 energy level while emitting a photon of wavelength 2.405 4 mm. Calculate (a) the moment of inertia of the H2 molecule about an axis through its center of mass and perpendicular to the H–H bond, (b) the vibrational frequency of the H2 molecule, and (c) the equilibrium separation distance for this molecule.arrow_forwardButadiene can be roughly modeled as a linear “box” with L = 0.424 nm. There are four electrons, two of which can go in each particle in a box state (two electrons in nX= 1; two electrons in nX= 2). The lowest excitation involves promoting an electron from nX= 2 to nX= 3. What is the energy of that excitation?arrow_forwardA space probe was designed to see 13CO in the atmosphere of Saturn by looking for lines in its rotational spectrum. If the bond length of CO is 112.8 pm, at what wave number do the first three rotational transitions appear?arrow_forward
- A rotating methane molecule is described by the quantum numbers J, MJ, and K. (a) For methane, how many rotational states have an energy equal to hBJ(J + 1) with J= 8? (b) Now consider chloromethane. How many rotationalstates have an energy equal to hBJ(J + 1) with J = 8?arrow_forwardA hydrogen atom rotates in three dimensions at a fixed distance of 100 pm from a fixed point. Ca lculate the energy of the level w ith rotational quantum number J = 1.arrow_forwardConsider an excited state configuration for He, 1s¹ 2p¹. (a) Find all the possible term symbols for this configuration. (b) Use Hund's rules to determine which of the term symbols obtained in (a) is the lowest energy state.arrow_forward
Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,