7E.3 The vibrational period of the C-H bond in tribromo- methane, CHBг3, is 91.2 ps. Treating the molecule as an oscil- lating H atom and a stationary CBг3 group, calculate the force constant for the C-H bond.
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7E.3
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- The first five vibrational energy levels of ¹H¹27 I are at 1144.83, 3374.90, 5525.51, 7596.66, and 9588.35 cm¹. Treating the molecule as an anharmonic oscillator, estimate the dissociation energy of the molecule in units of reciprocal centimetres (cm-¹). [Note: m(¹H) = 1.0078 u, m(¹271) = 126.9045 u; assume the second order anharmonicity constant, Ye, to be zero.] [Note: Use graph paper in your answer.]Determine the CO and CS bond lengths in OCS from the rotational constants B (16O12C32S) = 6081.5 MHz, B (16O12C34S) = 5932.8 MHz.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.
- A diatomic molecule has a rotational constant of 8.0 cm-1, and vibrational frequency of 1200 cm 1. What is the energy of the state with v = 1 and j = 6 relative to the lowest energy state, E = E(v=0,j=0)? 0(Slightly modified McQuarrie 5-41) Many quantum vibrational states are available to molecules. This raises the question: In what vibrational states are molecules actually found? Using sta- tistical mechanics, one can show (see McQuarrie 5-40 if you are interested) that the fraction of molecules in the n-th state is given by: fn = (1-e-hv/kBT) e -nhv/kBT where kB is the Boltzmann constant, kg = 1.380658 × 10-23 J/K. Compute the occupancy of the n=0, 1 and 2 states at 300 K and 1500 K for a "typical" harmonic frequency, we = 2650 cm-1. For practical purposes, what vibrational state is a typical molecule found in?can you please answer this step wise using G(v)
- A molecule in a liquid undergoes about 1.0 × 1013 collisions in each second. Suppose that (i) every collision is effective in deactivating the molecule vibrationally and (ii) that one collision in 100 is effective. Calculate the width (in cm−1) of vibrational transitions in the molecule.(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.E11C.2(a) Calculate the percentage difference in the fundamental vibrational wavenumbers of "Na Cl and "Na"Cl on the assumption that their force constants are the same. The mass of "Na is 22.9898m..
- Vibrational frequency of iodine molecule Br2 is 414 cm^-1. Calculate ratio populations of 1st excited to ground vibrational states in Br25. The rotational constant of 127135Cl is 0.1142 cm-1. (a) What is the most highly populated rotational level for the 127135CI molecules at 25 °C? (b) Calculate the bond length in the molecule. (c) Draw the rotational spectrum showing all absorptions in the region from 0 cm 1 to 10 cm 1.A molecule in a gas undergoes 2e+09 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally. Calculate the linewidth of rotational transitions in the molecule. (b) Suppose that 6 collisions in 10 are effective. MHz Submit Answer XMH