Let’s try building a one-dimensional crystal lattice from the scratch. Consider an atomic nucleus carrying Z number of protons. Assume that the Coulomb’s law holds in this situation. We take many of such nuclei and start placing them at a distance a from each other along a straight line. So, we end up constructing a very long (perhaps, infinite if we could actually have an infinite number of nuclei) straight chain of equi-spaced nuclei. Can you approximately draw the potential energy seen by a free electron in this lattice? A free electron is the one that is free to roam around the lattice, just like the ones in a metal. A good way to attack this problem would be to start by drawing the potential energy of the electron when there was just one nucleus present. After this, you can think that when you bring the nuclei close, they start sensing
Let’s try building a one-dimensional crystal lattice from the scratch. Consider an atomic nucleus carrying Z number
of protons. Assume that the Coulomb’s law holds in this situation. We take many of such nuclei and start placing them
at a distance a from each other along a straight line. So, we end up constructing a very long (perhaps, infinite if we could
actually have an infinite number of nuclei) straight chain of equi-spaced nuclei. Can you approximately draw the potential
energy seen by a free electron in this lattice? A free electron is the one that is free to roam around the lattice, just like
the ones in a metal. A good way to attack this problem would be to start by drawing the potential energy of the electron
when there was just one nucleus present. After this, you can think that when you bring the nuclei close, they start sensing
each others’ presence through the electric field.
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