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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- 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.Calculate the contribution of each normal mode to the molar vibrational heat capacity of H_2O (g) at 600 K.
- Estimate the centrifugal distortion constant for 1H127I, for which ᷉ B = 6.511 cm−1 and ᷉v = 2308 cm−1. By what factor would the constant change when 2H is substituted for 1H?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.Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.
- Estimate the values of γ = Cp,m/CV,m for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C? Hint: Note that Cp,m − CV,m = R for a perfect gas.The rotational constant for CO is 1.9314 cm−1 and 1.6116 cm−1 in the ground and first excited vibrational states, respectively. By how much does the internuclear distance change as a result of this transition?The vibrational wavenumber of Br2 is 323.2 cm−1. Evaluate the vibrational partition function explicitly (without approximation) and plot its value as a function of temperature. At what temperature is the value within 5 per cent of the value calculated from eqn 13B.16, which is valid at high temperatures?
- Calculate the relative populations of a linear rotor at 298 K in the levels with J = 0 and J = 5, given that ᷉ B = 2.71 cm−1.Consider the rotational temperatures of the following hetero diatomic molecules: θr(CO) = 2.1 K, θr(HF) = 30.2 K. In which case would the classical approximation be accurate? Justify your answer.Estimate the centrifugal distortion constant for 79Br81Br, for which ᷉ B = 0.0809 cm−1 and ᷉v = 323.2 cm−1. By what factor would the constant change when the 79Br is replaced by 81Br?