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The following are sets of rotational quantum numbers
(a)
(c)
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Chapter 14 Solutions
Physical Chemistry
- What 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_forward8C.4 (a) the moment of inertia of a CH4 molecule is 5.27 x 10^-47 kg m^2. What is the minimum energy needed to start it rotating? 8C.5 (a) use the data in 8C.4 (a) to calculate the energy needed excite a CH4 molecule from a state with l=1 to a state with l=2arrow_forwardIs the bond length in 1HCl the same as that in 2HCl? The wavenumbers of the J = 1 ← 0 rotational transitions for 1H35Cl and 2H35Cl are 20.8784 and 10.7840 cm–1, respectively. Accurate atomic masses are 1.007 825mu and 2.0140mu for 1H and 2H, respectively. The mass of 35Cl is 34.968 85mu. Based on this information alone, can you conclude that the bond lengths are the same or different in the two molecules?arrow_forward
- Calculate the possible ESR transitions between these states for S=1/2 and I=2arrow_forwardChoose the correct answers and give a short explanation. In microwave spectra: - the separation of 2 lines in the spectrum for HF is less than for DF - the rotation constant for the HF molecule is greater than for DF (D: deuterium) - the spectrum lines separate as the rotational number increases - energy levels approach as the rotational quantum number increasesarrow_forwardJ.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.arrow_forward
- Calculate the value of ml for a proton constrained to rotate in a circle of radius 100 pm around a fixed point given that the rotational energy is equal to the classical average energy at 25 degrees C.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_forwardThis question pertains to the heteronuclear diatomic 1H19 Given that the bond length of 1H19F is 0.91 angstrom (1 angstrom = 10-10m), calculate the moment of inertia. Calculate the rotational constant (in J) for the diatomic in part a. Using your value for the rotational constant in part b, determine the energy of the transition from state 3 to state 4 (in J). Do you expect the energy of the transition from state 3 to state 4 for 2H19F to be larger or smaller than what you computed in part c, assuming that the bond length does not change? Explain your choice based on the relevant equations, or calculate the energy for this transition. Steps 1, 2 and 3 have already been found. I need help with the last question only but I haven't been able to get it solved since there can only be three questions answered. The following answers for step 1-3 are below. 1. moment of inertia = 1.30 × 10-47 kgm2 2. rotational constant = 21.5 cm-1 3. Energy required from transition n= 3 to n= 4 is…arrow_forward
- : A space probe was designed to seek carbon monoxide in Saturn’s atmosphere by looking for lines in its rotational spectrum. If the bond length of CO is 112.8 pm, at what wavenumbers (in cm-1) do the first three rotational transitions appear? Carbon is almost all carbon-12, so for this part, you can assume it’s all 12C). What resolution would be required to determine the isotropic ratio of 13C to 12C on Saturn by observing the first three 13CO rotational lines as well? (In other words how far apart, in cm-1, are the rotational transitions of 12CO and 13COarrow_forwardAn 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_forwardUsing the rigid rotor model, calculate the energies in Joules of the first three rotational levels of HBr, using for its moment of inertia I = μR2, with μ = mHmX/(mH + mX) and equilibrium internuclear distance = 1.63 Å. To put these energies into units that make sense to us, convert energy to kJ/mol. (Simply estimate atomic masses from the average atomic weights of the elements given in the periodic table).arrow_forward
Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,
Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning