Problem A sodium atom ( Z =11) contains 11 protons in its nucleus. Strictly spea

Question

Problem A sodium atom (Z =11) contains 11 protons in its nucleus. Strictly speaking,The Bohr model does not apply, because the neutral atom contains 11electrons instead of a single electron. However, we can apply themodel to the outermost electron as an approximation, provided thatwe use an effective value Zeffective ratherthan 11 for the number of protons in the nucleus.

(a1) The ionization energy for the outermostelectron in a sodium atom is 5.1 eV. Use the Bohr model withZ = Zeffective tocalculate a value for Zeffective.

Explanation / Answer

For hydrogen En = -EI /n2 = -(k2 e4 m) / [2n2 (h / 2)2] For a nuclear charge of Z  the term e4becomes (Z e2)2 This gives us En = -Z2 EI / n2 for an atomlike sodium where EI is the ionization potential Z = (En n2 /EI ) = (5.1 * 32 / 13.6 ) =1.84 n here equals 3 because it represents the 11'th electron This is equivalent to a hydrogen-like atom in the n = 3 statewith a nuclear charge of Z = 1.84 This means that the outer electron in sodium is not completelyshielded from the nucleus by the 10 inner electrons. Hope this clears this up somewhat! This gives us En = -Z2 EI / n2 for an atomlike sodium where EI is the ionization potential Z = (En n2 /EI ) = (5.1 * 32 / 13.6 ) =1.84 n here equals 3 because it represents the 11'th electron This is equivalent to a hydrogen-like atom in the n = 3 statewith a nuclear charge of Z = 1.84 This means that the outer electron in sodium is not completelyshielded from the nucleus by the 10 inner electrons. Hope this clears this up somewhat!

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