A one-dimensional particle-in-a-box may be used to illustrate the import kinetic energy quantization in covalent bond formation.
For example, the electronic energy change associated with the reaction H+H H2 may be modeled by treating each reactant H atom as an electron in a one-dimensional box of length LH 5a0 (the 99% electron density diameter of hydrogen), and treating he diatomic H2 as a one-dimensional box of length LH2 RB+5ao (where ao is the Bohr radius of hydrogen and Re 0.74 Å is the experimental bond length of H2). (a) Use the above particle-in-a-box model to model ance of predict the bond formation energy of H2, and compare your result with the experi- mental value of -436 kJ/mol. (b) What interactions have been neglected in the above calculation and what does your result imply with regard to the importance of kinetic energy quantization in covalent bond formation?
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Answer:
Explanation:
The fusion reaction in this problem is
The total energy released in the fusion reaction is given by
where
is the speed of light
is the mass defect, which is the mass difference between the mass of the reactants and the mass of the products
For this fusion reaction we have:
is the mass of one nucleus of hydrogen
is the mass of one nucleus of helium
So the mass defect is:
The conversion factor between atomic mass units and kilograms is
So the mass defect is
And so, the energy released is: