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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.
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- Calculate the relative populations of a spherical rotor at 298 K in the levels with J = 0 and J = 5, given that ᷉ B = 2.71 cm−1.Find the oscillation amplitude of a diatomic molecule (CO) for n=1,2,3,4 & 10,when k=1926 N\m and reduced mass= 6.86 aDevelop an expression for the value of J corresponding to the most highly populated rotational energy level of a diatomic rotor at a temperature T remembering that the degeneracy of each level is 2J + 1. Evaluate the expression for ICl (for which ᷉ B = 0.1142 cm−1) at 25 °C. Repeat the problem for the most highly populated level of a spherical rotor, taking note of the fact that each level is (2J + 1)2-fold degenerate. Evaluate the expression for CH4 (for which ᷉ B = 5.24 cm−1) at 25 °C. Hint: To develop the expression, recall that the first derivative of a function is zero when the function reaches either a maximum or minimum value.
- Calculate the relative populations of a linear rotor in the levels with J = 0 and J = 5, given that B = 2.71 cm-1 and a temperature of 298 K.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.What is the most highly populated rotational level of Cl2 at (i) 25 °C, (ii) 100 °C? Take ᷉ B = 0.244 cm−1.
- Estimate the vibrational frequency and rotational constant for DBr. Provide a numerical answer in cm-1. Assume the bond length is 1.945 Å and the reduced mass is 1.95 amu.Consider 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?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?
- Pure rotational Raman spectra of gaseous C6H6 and C6D6 yield the following rotational constants: ᷉ B(C6H6) = 0.189 60 cm−1, ᷉ B(C6D6) = 0.156 81 cm−1. The moments of inertia of the molecules about any axis perpendicular to the C6 axis were calculated from these data as I(C6H6) = 1.4759 × 10−45 kg m2, I(C6D6) = 1.7845 × 10−45 kgm2. Calculate the CC and CH bond lengths.The rotational constant of 1H35CI is 317.8 GHz. What is the separation of the lines in its pure rotational spectrum (a) in gigahertz. (b) in reciprocal centimetres?Calculate 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.