(ii) Using the rigid rotor model draw a sketch of the rotational spectrum for each molecule indicating the selection rules. Reduced Mass $\large \mu = \frac{m_1 m_2}{m_1 + m_2} $ It mainly depends on the distribution of mass around an axis of rotation. Using the rotational constants from the polynomial curve fit with the definition of B gives the moment of inertia 19. Calculate the moment of inertia for HCl molecule from the given value of rotational constant, B = 10.40 cm. Harmonic oscillator expression Allows us to find the “spring” force constant for HCl and DCl k = 514.96 N/m 18. Definition. The characteristic rotational temperature (θ R or θ rot) is commonly used in statistical thermodynamics to simplify the expression of the rotational partition function and the rotational contribution to molecular thermodynamic properties. The SI unit of moment of inertia is kg m 2. View Winning Ticket Calculate the moment of inertia of an HCl molecule from its infrared absorption spectrum shown in Figure 43.9. 2. | EduRev GATE Question is disucussed on EduRev Study Group by 167 GATE Students. 10 61. where, the moment-of-inertia, I, is given by . (C) 2.68 Can you explain this answer? It is an extensive property of any object. Table of Content. The degeneracy of the Jth quantum level is 2J+1. The rotational energies, as we shall see, depend on the rotational constants designated by A, B, and C, with A > B > C, and defined by h h „ h MOI varies depending on the axis that is chosen. The moment of inertia of HCl molecule about an axis passing through its centre of mass and perpendicular to the line joining the H and Cl ions will be, if the interatomic distance is 1 Å (a) 2 47. Frequencies. ( moment nert a out principal axis given 2by Iǁ = 2m H R (1‐cosϴ) where the mass of hydrogen atom m H =1.6735*10‐27 kg, 10the N‐H bond length r= 1.014*10‐ m and the bond angle is 106 780The106.780.The moment of inertia abo tabout principal aisaxis is I ǁ) Go to your Tickets dashboard to see if you won! The total canonical partition function of a system of identical, indistinguishable, noninteracting atoms or molecules can be divided into the atomic or molecular partition functions : =! for I, the moment of inertia of the HCl molecule. Calculate I, the moment of inertia, for HCl and HBr and the interatomic distances. 10 061. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation. Where; the moment of inertia for a molecule (I) = Then; I = m .r 2 = Σ m .r2 i i i Where: r i is the perpendicular distance of the atom i from the axis of rotation (bond length). The absorption lines shown involve transitions from the ground to first excited vibrational state of HCl… - 22836110 Determine the fundamental vibrational frequency of HCl and DCl. Ie is a molecular constant called the moment of inertia, which for a diatomic molecule is Ie = mre 2, and m and r e are, in turn, the reduced mass, (see above) and the equilibrium bond length of the molecule AB. Since the moment of inertia is dependent on the bond length, it too changes and, in turn, changes the rotational constant B. Calculate moment of inertia of this molecule, and then use it to calculate the energies of the AEo-1 and AE_2 transitions for both the 2D and 3D rotor in J. Moment of Inertia I = mr2. A classic among molecular spectra, the infrared absorption spectrum of HCl can be analyzed to gain information about both rotation and vibration of the molecule. (i) Do these molecules have a pure rotational spectrum? 1-+2 where I is the moment of inertia shown in Eq. 0 m kg (b) 2 47. 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