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Problem: The electronic band structure of nickel.If the metal were potassium rather than nickel, which bands- 4s, 4p, and/or 3d -would be partially occupied?

FREE Expert Solution

We have to determine which of the bands shown in the diagram (4s, 4p, and/or 3d) would be partially occupied in case of potassium metal.

To determine the band, we need to know which orbital of potassium has its valence electrons.

We will write the electron configurationof potassium metal.

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Problem Details

A diagram has energy, increasing on the y-axis with the atomic orbitals of a single nickel atom on the x-axis (energy increases from 4s orbitals to the 3d orbitals to the 4p orbitals). In the 4s orbitals there are two electrons, one pointing up and one pointing down. In the 3d orbitals there are two single arrows pointing up, then three pairs of electrons with one up and one down in each. In the 4p orbitals there are no electrons. The band structure of nickel crystal shows molecular orbitals, with a dotted line separating filled molecular orbitals from empty molecular orbitals. Molecular orbitals become increasingly bonding moving down in the lower half of the diagram and molecular orbitals become increasingly antibonding moving up in the upper half of the diagram. The thin 4s band holds two electrons per atom (filled); the large 3d band holds 10 electrons per atom (mostly filled with 8 electrons) and the medium width 4p band holds 6 electrons per atom (unfilled).

The electronic band structure of nickel.

If the metal were potassium rather than nickel, which bands- 4s, 4p, and/or 3d -would be partially occupied?

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Based on our data, we think this problem is relevant for Professor Donnelly's class at UCF.