Concept explainers
(a)
Interpretation:
The expected ratios of molecules in odd rotational states to even rotational stated for given molecule is to be predicted.
Concept introduction:
The antisymmetric spin states represent the even rotational states while symmetric spin states represent the odd rotational states.
The odd rotational states are calculated by,
The even rotational states are calculated by,
Where,
•
(b)
Interpretation:
The expected ratios of molecules in odd rotational states to even rotational stated for given molecule is to be predicted.
Concept introduction:
The antisymmetric spin states represent the even rotational states while symmetric spin states represent the odd rotational states.
The odd rotational states are calculated by,
The even rotational states are calculated by,
Where,
•
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Physical Chemistry
- Calculate the relative number of molecules in the J = 1 and J = 2 rotational states of HCI at 27 \deg C. (I = 2.643 x 1047 kg m^2).arrow_forwardThe vibrational temperature of a molecule prepared in a supersonic jet can be estimated from the observed popula- tions of its vibrational levels, assuming a Boltzmann distri- bution. The vibrational frequency of HgBr is 5.58 × 1012 s-1, and the ratio of the number of molecules in the n = 1 state to the number in the n = 0 state is 0.127. Estimate the vibra- tional temperature under these conditions.arrow_forward(c) Consider the following rotational temperatures of diatomic molecules: qr(N2) = 2.9K, qr(HD) = 64.7K Assuming classical behaviour (i.e. continuum approximation): (i) Estimate the number of accessible rotational energy levels at 290 K for both moleculesarrow_forward
- 3. Consider a 2 × 2 square lattice of spins interacting via the Ising Hamiltonian in the absence of a magnetic field: H = - ΣSi Sj, (ij) we have set J = 1. (a) Write down all the possible configurations and calculate the energy for each one of them. (b) Calculate the partition function Z, as a function of temperature, by summing over all configurations. (c) Repeat question (3a) and (3b), using periodic boundary condi- tions.arrow_forwardConsider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?arrow_forwardCalculate the CO and CS bond lengths in OCS from the rotational constants B(16O12C32S) = 6081.5MHz, B(16O12C34S) = 5932.8MHz.arrow_forward
- 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.arrow_forwardA molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally and (b) that one collision in 10 is effective. Calculate the width (in cm³¹) of rotational transitions in the molecule.arrow_forwardDerive 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.arrow_forward
- 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.arrow_forwardCalculate the relative populations of the J = 2 and J = 1 rotational levels of HCI at 25 oC. For HCI the rotational constant is B =318.0 GHz.arrow_forward(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.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,