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5) (1) Knowing that lithium crystallizes in a cubic system with lattice considering its atomic mass (7) and its volumetric mass (546 kg-m-3), find which one is it ([simple cubic, body- centered cubic (bcc), or face-centered cubic (fcc)]?

5) (1) Knowing that lithium crystallizes in a cubic system with lattice considering its atomic mass (7) and its volumetric mass (546 kg-m-3), find which one is it ([simple cubic, body- centered cubic (bcc), or face-centered cubic (fcc)]?

Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter21: Structure And Bonding In Solids
Section: Chapter Questions
Problem 23P
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Hi, Can you please solve the question and make explanation step by step? Just Option 1

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5) (1) Knowing that lithium crystallizes in a cubic system with lattice considering its atomic mass (7) and its volumetric mass (546 kg-m-³), find which one is it ([simple cubic, body- centered cubic (bcc), or face-centered cubic (fcc)]? (2) Knowing that the valence electrons of this metal (1 per atom) behave as free electrons, find the shape of the Fermi surface and its expression and then calculate its characteristic dimension ke. (3) Compare kɛ obtained in (2) to the distance dm, which in reciprocal space separates the origin from the first boundary of the first Brillouin zone nearest the origin. (Evaluate dm using simple geometric considerations without having to sketch the first Brillouin zone.) (4) Find the Fermi energy of lithium Er, the Fermi temperature TF, and the speed of wF of the fastest free electrons. (5) Knowing that the resistivity p of lithium is of the order 10-5 N cm at ambient temperature, find the time of flight, t, and the mean free path A of conduction electrons. (6) Find the drift velocity va of conduction electrons subject to a electric field of 1 V/m and compare it with the Fermi velocity VF. (7) Starting from the relation ke =1/3 CaVFA (or with the help of the Wiedemann-Franz expression), find the thermal conductivity due to electrons Ke of lithium at ambient temperature T = 300 K.
Transcribed Image Text:5) (1) Knowing that lithium crystallizes in a cubic system with lattice considering its atomic mass (7) and its volumetric mass (546 kg-m-³), find which one is it ([simple cubic, body- centered cubic (bcc), or face-centered cubic (fcc)]? (2) Knowing that the valence electrons of this metal (1 per atom) behave as free electrons, find the shape of the Fermi surface and its expression and then calculate its characteristic dimension ke. (3) Compare kɛ obtained in (2) to the distance dm, which in reciprocal space separates the origin from the first boundary of the first Brillouin zone nearest the origin. (Evaluate dm using simple geometric considerations without having to sketch the first Brillouin zone.) (4) Find the Fermi energy of lithium Er, the Fermi temperature TF, and the speed of wF of the fastest free electrons. (5) Knowing that the resistivity p of lithium is of the order 10-5 N cm at ambient temperature, find the time of flight, t, and the mean free path A of conduction electrons. (6) Find the drift velocity va of conduction electrons subject to a electric field of 1 V/m and compare it with the Fermi velocity VF. (7) Starting from the relation ke =1/3 CaVFA (or with the help of the Wiedemann-Franz expression), find the thermal conductivity due to electrons Ke of lithium at ambient temperature T = 300 K.
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