a. First, derive a general expression for the energy gab using this model. In other words, calculate the difference in energy Δ E between state n+1 and state n using the constants m, L, and h. b. Assuming the transition occurs from the lowest energy state to the second state (n=1 --> n=2), estimate the length of the solvent pocket where the electron is confined. Report your answer in angstroms. Use your expression from part c. c. Higher level calculations have suggested the size of the box is approximately 11 angstroms. Based on this information and your answer to part d, comment on whether the particle in a box model provides a reasonable first approximation.
When sodium metal dissolves in compressed liquid ammonia, a highly conductive blue solution is formed. This effect occurs because of solvated electrons that are effectively confined within a packet of solvent molecules. In this question, we will estimate the properties of this system.
a. First, derive a general expression for the energy gab using this model. In other words, calculate the difference in energy Δ E between state n+1 and state n using the constants m, L, and h.
b. Assuming the transition occurs from the lowest energy state to the second state (n=1 --> n=2), estimate the length of the solvent pocket where the electron is confined. Report your answer in angstroms. Use your expression from part c.
c. Higher level calculations have suggested the size of the box is approximately 11 angstroms. Based on this information and your answer to part d, comment on whether the particle in a box model provides a reasonable first approximation.
d. How does the energy gap between states depend on the size of the box? In other words, how does the difference in energy Δ E relate to the length of the box L?
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