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2. The diagram below shows the potential energy of an oxygen molecule (O₂) as a function of the separation x between the two oxygen nuclei. (As usual, the potential energy is defined to be zero when the two nuclei are very far apart.) If the molecule absorbs a single ultraviolet photon of wavelength 185 nm (which is a common wavelength used by germicidal lamps that sterilize surfaces), the total energy of the system increases by 11 x 10-1⁹ J. If the system's ground state energy is (approximately) equal to the minimum energy on the potential energy curve, is one photon enough to split the molecule apart? If so, what is the kinetic energy of each of the two oxygen atoms after the molecule has split (assume that they each get the same kinetic energy)? If not, what is the minimum photon energy that would split the molecule? U (10-¹⁹) 12 T. x(nm) 0.4 0.2 0.3 8 4 0 -4 -8 0.0 0.1
a. The system's total energy can be represented as a horizontal line on the graph. What determines whether the line corresponds to a molecule with enough energy to split? b. What is the system's total energy before it absorbs the photon? What about after it absorbs the photon? Is this enough to split the molecule? c. Use your value for the total energy after the photon is absorbed to determine either the kinetic energy of each of the two oxygen atoms after the molecule has split or the minimum photon energy that would split the molecule. d. For the energy diagram shown in problem 2, sketch a plot on the axes below of the force between the two oxygen nuclei as a function of their separation x. Represent a repulsive force (i.e. one that tends to increase x, to the left in the diagram) as positive and an attractive force as negative. Your sketch does not have to be quantitatively accurate, but it should show approximately where the force is positive, where it is negative, where it crosses zero, and the general trend of whether the force is increasing or decreasing in magnitude.