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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.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.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 a
- Develop 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.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 Br2 at (i) 25 °C, (ii) 100 °C? Take ᷉ B = 0.0809 cm−1.
- 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?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?
- 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.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.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?