The potential energy for a diatomic molecule has a minimum

Chapter , Problem 12

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The potential energy for a diatomic molecule has a minimum as shown in Figure 37-13. Near this minimum, the graph for the energy as a function of distance between the atoms may be approximated as a parabola, leading to the harmonic oscillator model for the vibrating molecule. An improved approximation is called the anharmonic oscillator and leads to a modification of the expression for the energy where (Equation 37-18). The modified expression for energy is where For an molecule, the constants have the values and Use this formula to estimate the smallest value of the quantum number for which the modified expression differs from the original expression by 10 percent.