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- 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?Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius RCalculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.
- If a nitrogen molecule is trapped in a hypothetical 1-D box of length 1.10 cm, at what value of the translational quantum number, n does the translational energy of the molecule becomes equal to 1/3 kT at 350 K?1. [10] Consider an adsorption band in the combined rotational-vibrational spectrum of a linear molecule, where the fundamental vibrational frequency involved in the observed band is 2325 cm-¹ and the rotational constant of the molecule is B=2.4 cm³. Say hypothetically, the specific selection rules for the rotational states are AJ = ±2. At what wave numbers would the first three peaks that occur at both higher and lower wave numbers than fundamental vibrational frequency occur at? What transitions would each peak correspond to?The rotational constant of 12C16O is 57.65 GHz. Calculate the value of J for the most populated level at (a) 300 K and (b) 1000 K.
- A molecule of NH3 diffuses at 1.50 m from a point source. If a molecule of N2 would diffuse under the same condition for the same period, find the distance that a molecule of N2 will cover.J.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.Derive an expression for the mean energy of a collection of molecules that have three energy levels at 0, ε, and 3ε with degeneracies 1, 5, and 3, respectively.
- The moment of inertia of CH4 can be calculated from the expression I=8/3 mHR2 where R is the C-H bond length (109 angstrom or 109 x 1012 m). a. What is the lowest possible rotational energy of the CH4 molecule and what is the value of quantum number l associated with that rotational energy? b. Calculate the rotational energy of the molecule in the first excited state (when quantum number l = 1). c. Determine the degeneracy of the first excited state. Explain what is meant by rotational energy degeneracy.(c) When a gas is expanded very rapidly, its temperature can fall to a few degrees Kelvin. At these low temperatures, unusual molecules like ArHCl (Argon weakly bonded to HCl) can form on mixing. For the isotopic species Ar H$CI, the following rotational transitions were observed: J (1 → 2): 6714.44 MHz J (2 → 3): 10068.90 MHz Assume the molecule can be treated as a linear diatomic molecule (ArCl). (i) Calculate the rotational constant (B) and centrifugal distortion (D) constant for this molecule.Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.