Consider this simple model for lithium, which has two n=1 electrons and a lone n=2 valence electron.

1. Find the approximate orbit radius in terms of ao of each of the n=1 electrons orbiting three protons.
2. What would be the energy of a single n=1 electron if it were orbiting the nucleus alone?
3. The two n=1 electrons, being in the same spatial state, must have the same energy and orbit radius. To account for the repulsion between them, assume that they are roughly one orbit diameter apart and that they split this repulsive energy equally. What is the new approximate energy of the electrons?
4. Assuming the n=1 electrons shield/cancel out two of the protons in lithium's nucleus, find the energy and orbit radius of an n=2 electron orbiting a net charge of just +e. Remember that the lowest energy state will be the lower n value.
5. Use your results from the previous questions to justify why lithium's valence electron is "easily given up" and why we are justified in dismissing the role of the n=1 electrons in chemical reactions. Why would the valence electron be farther from the nucleus for other alkali metals?

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