Consider HCN, which has three features in its IR spectrum: 946, 2380, and -1 3386 cm¹. (a) Sketch the motions of each normal mode and denote any degeneracies. (b) Assign each feature in the IR spectrum to a normal mode of the molecule. (c) Determine the zero-point energy of HCN.
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- Write a Slater determinant for the lithide ion, Li.(A) Explain why the spacings between the bands in the vibrational spectrum of a diatomic molecule would be expected to decrease with increasing vibrational quantum number. (B) Explain why a molecule with no dipole moment is microwave inactive but may show an infrared spectrum. (C) Explain the occurrence of P and R branches in the rotational fine structure of a vibrational transition of a diatomic molecule such as HCl or CO.8C.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=2
- (a) Look very carefully at the pictures below: Picture 1 and Picture 2. What does each of the pictures represent? Give FULL EXPLANATIONS for your answer. (1) (2) (b) Look very carefully at the picture below. Give the relevant quantum numbers. Explain your answer. у-аxis (c) (i) What is a wavefunction? (ii) What are the two parts of a wavefunction? (iii) What is the importance of squaring a wavefunction? (iv) Where is a wavefunction obtained from?Rotational 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?(a) For C6H6, the number of vibrational modes is ??? (b) For titanium (Z=22), its electron configuration for the ground state is ??? (c) For ³D, (i) the possible values of J are ??? and (ii) the total degeneracy is ???
- β-Carotene (1) is a linear polyene in which 10 sing le and 11 double bonds alternate along a chain of 22 carbon atoms. If the length of each CC bond is taken to be about 140 pm , then the length L of the molecular box in β-carotene is L = 2.94 nm. Estimate the wavelength of the light absorbed bythis molecule when it undergoes a t rans it ion from its ground state to the next higher excited state.3. ^14N^16O (the superscripts represent the atomic mass number) (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bondThe 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).
- Ca lcu late the size of the quantum involved in the excitation of (a) an electronic motion of frequency 1.0 x 1015 Hz. (b) a molecular vibration of period 20 Is. (c) a pendulum of period 0.50 s. Express the results in joules and in kilojoules per mole.Calculate the energy contributions to the 1s2p (first) excited state of Helium due to the interaction between electrons.Bohr’s model can be used for hydrogen-like ions—ions thathave only one electron, such as He + and Li2 + . (a) Why isthe Bohr model applicable to He + ions but not to neutral Heatoms? (b) The ground-state energies of H, He + , and Li2 + aretabulated as follows:By examining these numbers, propose a relationship betweenthe ground-state energy of hydrogen-like systems and thenuclear charge, Z. (c) Use the relationship you derive in part(b) to predict the ground-state energy of the C5 + ion.