Calculate the relative numbers of Cl2 molecules ( ᷉v = 559.7 cm−1) in the ground and first excited vibrational states at (i) 298 K, (ii) 500 K.
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Calculate the relative numbers of Cl2 molecules ( ᷉v = 559.7 cm−1) in the ground and first excited vibrational states at (i) 298 K, (ii) 500 K.
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- 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.Estimate the ratio of the number of molecules in the first excited vibrational state of the molecule N2 to the number in the ground state, at a temperature of 450 K. The vibrational frequency of N2 is 7.07 × 1013 s-1.The vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 cm−1, whereas that in the excited state (B 3Σu−), to which there is an allowed electronic transition, is 700 cm−1. Given that the separation in energy between the minima in their respective potential energy curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from the v = 0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.
- Calculate the relative numbers of Br2 molecules ( ᷉v = 321 cm−1) in the second and first excited vibrational states at (i) 298 K, (ii) 800 K.Estimate the ratio of the number of molecules in the firstexcited vibrational state of the molecule N2 to the numberin the ground state, at a temperature of 450 K. The vibrational frequency of N2 is 7.07 × 1013 s-1.The J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011 Hz.(A) Use this information to calculate the moment of inertia of the molecule. (B) Calculate the bond length of the molecule.
- 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 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.]Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.
- (a) Express the moment of inertia of an octahedral AB6 molecule in terms of its bond lengths and the masses of the B atoms. (b) Calculate the rotational constant of 32S19F6 , for which the S—F bond length is 158 pm.What is the most highly populated rotational level of Cl2 at (i) 25 °C, (ii) 100 °C? Take ᷉ B = 0.244 cm−1.The first three absorption lines in the pure rotational spec- trum of gaseous 12C16O are found to have the frequencies 1.15 x 1011, 2.30 × 1011, and 3.46 × 1011 s-1. Calculate: (a) The moment of inertia I of CO (in kg m²) (b) The energies of the J = 1, J = 2, and J = 3 rotational levels of CO, measured from the J = 0 state (in joules) (c) The C-O bond length (in angstroms)