1. Square lattice, free electron energies. (a) Show for a simple square lattice (two dimensions) that the kinetic energy of a free electron at a corner of the first zone is higher than that of an electron at midpoint of a side face of the zone by a factor of 2. (b) What is the corresponding factor for a simple cubic lattice (three dimensions)? (c) What bearing might the result of (b) have on the conductivity of divalent metals?
1. Square lattice, free electron energies. (a) Show for a simple square lattice (two dimensions) that the kinetic energy of a free electron at a corner of the first zone is higher than that of an electron at midpoint of a side face of the zone by a factor of 2. (b) What is the corresponding factor for a simple cubic lattice (three dimensions)? (c) What bearing might the result of (b) have on the conductivity of divalent metals?
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![1. Square lattice, free electron energies. (a) Show for a simple square lattice (two
dimensions) that the kinetic energy of a free electron at a corner of the first zone is
higher than that of an electron at midpoint of a side face of the zone by a factor of 2.
(b) What is the corresponding factor for a simple cubic lattice (three dimensions)?
(c) What bearing might the result of (b) have on the conductivity of divalent metals?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba5d1c9-d402-4ab6-82b5-baa3f495e3dc%2F8263b450-5961-4266-8a77-55ca07d4f9e7%2Fezgegrh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Square lattice, free electron energies. (a) Show for a simple square lattice (two
dimensions) that the kinetic energy of a free electron at a corner of the first zone is
higher than that of an electron at midpoint of a side face of the zone by a factor of 2.
(b) What is the corresponding factor for a simple cubic lattice (three dimensions)?
(c) What bearing might the result of (b) have on the conductivity of divalent metals?
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