Question Solved1 Answer 7.7 For a square lattice in two dimensions (a) Show that the kinetic energy of a free electron in a corner of the first Brillouin zone is a factor of two larger than that of an electron in the middle of the Brillouin zone edge. (b) Determine the corresponding factor for a primitive lattice in three dimensions. 12111

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Transcribed Image Text: 7.7 For a square lattice in two dimensions (a) Show that the kinetic energy of a free electron in a corner of the first Brillouin zone is a factor of two larger than that of an electron in the middle of the Brillouin zone edge. (b) Determine the corresponding factor for a primitive lattice in three dimensions. 12111
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Transcribed Image Text: 7.7 For a square lattice in two dimensions (a) Show that the kinetic energy of a free electron in a corner of the first Brillouin zone is a factor of two larger than that of an electron in the middle of the Brillouin zone edge. (b) Determine the corresponding factor for a primitive lattice in three dimensions. 12111
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At C,E_(c)=(ℏ^(2))/(2m)[((pi )/(a))^(2)+((pi )/(a))^(2)]=2(pi^(2)ℏ^(2))/(2ma^(2))(E_(c))/(E_(M))=2=>E_(c)=2E_(M)//jFor 3D AdrcostE=(ℏ^(2))/(2m)[k_(x)^(2)+k_(y)^(2)+k_(2)^(2)]{:[" At corner "E_(R)=(ℏ^(2))/(2m)[((pi )/(a))^(2)+((pi )/(a) ... See the full answer