hw_5_solu

hw_5_solu - ME 125NT Intro to Nanotechnology Due Solution...

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ME 125NT Intro to Nanotechnology Due: 5/8/2008 1 Solution Set 5 Problem 6.14 in book We can look at the band structure of an element to get an idea of how many electrons per atom participate in conduction. We can also determine this number based on the free electron density, the atomic mass, and the mass density of the material. (a) Calculate the free electron density of lithium. The Fermi energy is 4.72 eV. (b) Derive a formula for the number of atoms per unit volume. (c) Calculate the number of atoms per unit volume of lithium (535 kg/m 3 , 6.9 g/mol) using the formula you derived in part (b). (d) Determine the number of free electrons per lithium atom. (e) What is the electron configuration for Li? Explain whether your answer to (d) makes sense according to this configuration. The free electron(s) of Li is in which sublevel? ANSWER A) ( ) ( ) ( ) × × × = - 2 3 19 3 2 34 - 2 3 31 - J 10 56 7 3 2 s / kg m 10 6.626 kg 10 9.11 2 8 . n e π = 4.7 × 10 28 electrons/m 3 B) The number of atoms per unit volume = [kg/mol] ]) [kg/m ])( [atoms/mol (N 3 A A ρ , where N A is Avogadro’s number, ρ is the density of the material and A is the atomic mass. C) = × [kg/mol] 0069 0 ]) [kg/m 35 5 ])( [atoms/mol 10 (6.022 3 23 . 4.67 × 10
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This note was uploaded on 08/06/2008 for the course ME 125 taught by Professor Pennathur during the Spring '08 term at UCSB.

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hw_5_solu - ME 125NT Intro to Nanotechnology Due Solution...

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