What is the minimum energy needed to start it rotating 8C.5 (a) use the data in 8C. The equilibrium bond length of the molecule is 1.275. 8C.4 (a) the moment of inertia of a CH4 molecule is 5.27 x 10-47 kg m2. The masses of the two atoms are mH 1.673 x 10 27 kg and mCl 5.807 x 10 26 kg. The absorption peaks are due to transitions from the \(n = 0\) to \(n = 1\) vibrational states. Calculate the moment of inertia, I, of the molecule 1 H 35 Cl. Calculate the moment of inertia (I) for HCl and DCl using the following numbers and equation: H 1 g/mol D 2 g/mol Internuclear Distance 35 Cl 34 g/mol. where u is the atomic mass unit and is given by u 1.660539 10 24 g. Evaluation of the moment of inertia in HCl The bond length between H and Cl in HCl is r0 The mass of H is m(H) 1.00794 u. and each energy level has a degeneracy of 2J + 1 2 J + 1 due to the different mJ m J values. The effective force constant of a vibrating HCl molecule is k 5 480 N/m. Figure 5.9.5 : Two atoms connected by a vibrating bond. Hint: draw and compare Lewis structures for components of air and for water. Calculate (a) the moment of inertia of the H 2 molecule about an axis through. ![]() This stretching increases the moment of inertia and decreases the rotational constant (Figure 5.9.5 ). ![]() As the rotational angular momentum increases with increasing (J), the bond stretches. The effect of centrifugal stretching is smallest at low \(J\) values, so a good estimate for \(B\) can be obtained from the \(J = 0\) to \(J = 1\) transition.\). The moment of inertia is obtained as 2 I r0, where is the reduced mass and is defined by 1 2 1 2 m m mm. This decrease shows that the molecule is not really a rigid rotor. The correct option is BIf r1 and r2 are the respective distances of particles m1 and m2 from the centre of mass thenm1r1 m2r2 1×x 35.5×(Lx) x 35.5(1x) x 0.973o A and Lx 0.027o AMoment of inertia of the system about centre of mass I m2 x+m2(Lx)2I 1amu×(0.973o A)2+35.5amu×(0.027o A)2Substituting 1 a.m.u. ![]() A special rigid rotor is the linear rotor requiring only two angles to describe, for example of a. To orient such an object in space requires three angles, known as Euler angles. ![]() An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. However, the force exerted by the extended spring pulls the particles onto a periodic, oscillatory path. In rotordynamics, the rigid rotor is a mechanical model of rotating systems. \): In the absence of the spring, the particles would fly apart.
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