The energy expression for various rotational levels of a linear triatomic molecule is the same as that of a diatomic molecule. For 1H12C14N and 2D12C14N, the rotational constants are 44315.97 MHz and 36207.40 MHz, respectively. Assuming that the bond lengths are independent of isotopic substitution. Calculate the C-H and C - N bond lengths.

Calculate the HC and CN bond lengths in HCN from the rotational constants B(1H12C14N) = 44.316 GHz and B(2H12C14N) = 36.208 GHz.

Explain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.

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?

Calculate the rotational constant (B) for the molecule H12C14N, given that the H-C and C-N bond distances are 106.6 pm and 115.3 pm respectively.

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Explain why the lines in the spectrum for H35Cl and H37Cl give rise to different rotational constants for the two molecules.

The rotation of a 1H127I molecule can be thought of as the rotation of an H atom, which is confined to the surface of a sphere, about a stationary I atom, which is located at the centre of that sphere. The length of the HI bond is              1.6 × 10−10 m. Calculate the energies of the three lowest rotational energy levels and state their degeneracies.

The 14 N160 molecule undergoes a transition between its rotational ground state and its rotational first excited state. Approximating the diatomic molecule as a rigid rotor, and given that the bond length of NO is 1.152 Angstroms, calculate the energy of the transition. As your final answer, calculate the temperature T in Kelvin, such that Ethermal = kBT equals the %3D energy of the transition between NO's rotational ground state and fırst excited state.

Calculate the separation between the two lowest energy levels for an N2 molecule in a one- dimensional container of length 2.0 cm. At what value of n does the energy of the molecule reach ½kT at 300 K, and what is the separation of this level from the one immediately below?