Cesium is a monovalent metal having a density of 1.870 g/cm 3 and a molar mass o

Question

Cesium is a monovalent metal having a density of 1.870 g/cm3 and a molar mass of 132.9 g/mol. (a) Use this information to calculate the density of charge carriers.
electrons/m3

(b) Use this information to calculate the Fermi energy of cesium.
eV Cesium is a monovalent metal having a density of 1.870 g/cm3 and a molar mass of 132.9 g/mol. (a) Use this information to calculate the density of charge carriers.
electrons/m3

(b) Use this information to calculate the Fermi energy of cesium.
eV Cesium is a monovalent metal having a density of 1.870 g/cm3 and a molar mass of 132.9 g/mol. (a) Use this information to calculate the density of charge carriers.
electrons/m3

(b) Use this information to calculate the Fermi energy of cesium.
eV (a) Use this information to calculate the density of charge carriers.
electrons/m3

(b) Use this information to calculate the Fermi energy of cesium.
eV

Explanation / Answer

Given density of metal d= 1.870 g / c m3 molar mass m = 132.9g / mol number of density of conduction of electrons n = d / M here M = m / Avagadro's number = 132.9 g / mol / ( 6.022*1023 mol -1 ) = 2.2065416e-22 there fore n = 1.87 g / c m3 / (2.2065416e-22 = 8.4748006e+21 electrons cm-3 = 8.4748006e+21 ( 10-2 m )-3 = 8.4748006e+21 ( 10-2 m )-3 (10-7 ) 3 / ( 10 -7 ) 3 = 8.474 nm-3 __________________________________________________ The fermi energy for a metal is E F = ( 0.121 h2 / m ) n 2/3 = [( 0.121 )(6.625*10-34Js ) / 9.1*10-31 kg ) ] (8.474 nm-3 )2/3 = 2.425724e-37 J = 1.5140179 = 1.5140179

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