Question

Many diatomic (two-atom) molecules such as H2. 02, and N2 are bound together by covalent bonds. The interaction between two atoms can be described by a potential energy function of the following form, 2b Here, A, b, and ro are positive constants, and r is the center-to-center separation of the twa atoms. The mass of each atom is m CM Sketch U(r) versus r, and show that the two atoms are in stable equilibrium at r -ro- Find the total energy E of the molecule in the CM (center of mass) frame of the dr molecule. Express your answer in terms of r and v dt Find the equation of motion for r. Suppose that the two atoms oscillate about the equilibrium position with very small amplitudes. By making appropriate approximations to the equation of motion obtained in question (c), show that the displacement, x-r-ro, executes a simple harmonic motion, and find its angular frequency. In addition, calculate the numerical value of the angular frequency for H2 (the hydrogen molecule), with A-2.97x108 N, b 1.95x1010 m1, ro-7.4x1011 m, and m-1.67x1027 kg. Hint: For appropriate approximations, you may use the expansion e 1 uu2+. for small u. 2

Answer 1

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