PHYSICS F./SCI... W/MOD V.II W/KIT
4th Edition
ISBN: 9780134819884
Author: GIANCOLI
Publisher: PEARSON
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Question
Chapter 40, Problem 39P
(a)
To determine
Find the Fermi energy of one-dimensional metal.
(b)
To determine
Find the smallest amount of energy that this one-dimensional metal absorb.
(c)
To determine
Find the limit of
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Students have asked these similar questions
(c) Calculate the Fermi energy of silver from the
data given below:
atom.
Density of Silver = 10.5 gm/cm³
atomic weight = 108
h = 6.62×10-34 Joule - sec
m = 9.1×10-³1 Kg.
Avogadro's number =6.02×10-21 atoms/gm-
.In sodium there are about 2.6 x 1028 conduction electrons per cubic metre
which behave as a free electron gas. Fronm these facts estimate the Fermi
energy of the gas and an approximate value of the molar electronic heat
capacity at 300K.
(c)
Obtain expressions for the Fermi energy, the total energy and the density of states for a
free electron gas in one dimension. Show the variation of the density of states with
energy.
Chapter 40 Solutions
PHYSICS F./SCI... W/MOD V.II W/KIT
Ch. 40.4 - Determine the three lowest rotational energy...Ch. 40.6 - Prob. 1BECh. 40.6 - Prob. 1CECh. 40.8 - Prob. 1DECh. 40 - What type of bond would you expect for (a) the N2...Ch. 40 - Describe how the molecule CaCl2 could be formed.Ch. 40 - Does the H2 molecule have a permanent dipole...Ch. 40 - Although the molecule H3 is not stable, the ion...Ch. 40 - The energy of a molecule can be divided into four...Ch. 40 - Would you expect the molecule H2+ to be stable? If...
Ch. 40 - Explain why the carbon atom (Z = 6) usually forms...Ch. 40 - Prob. 8QCh. 40 - Prob. 9QCh. 40 - Prob. 10QCh. 40 - Prob. 11QCh. 40 - Prob. 12QCh. 40 - Prob. 13QCh. 40 - Prob. 14QCh. 40 - Prob. 15QCh. 40 - Prob. 16QCh. 40 - Prob. 17QCh. 40 - Prob. 18QCh. 40 - Prob. 19QCh. 40 - Prob. 20QCh. 40 - Prob. 21QCh. 40 - Prob. 22QCh. 40 - Prob. 23QCh. 40 - Prob. 1PCh. 40 - (II) The measured binding energy of KCl is 4.43eV....Ch. 40 - (II) Estimate the binding energy of the H2...Ch. 40 - (II) The equilibrium distance r0 between two atoms...Ch. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - (III) (a) Apply reasoning similar to that in the...Ch. 40 - (I) Show that the quantity 2/I has units of...Ch. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - (II) Calculate the bond length for the NaCl...Ch. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Prob. 30PCh. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 35PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 44PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60PCh. 40 - Prob. 61PCh. 40 - Prob. 62GPCh. 40 - Prob. 63GPCh. 40 - Prob. 64GPCh. 40 - Prob. 65GPCh. 40 - Prob. 66GPCh. 40 - Prob. 67GPCh. 40 - Prob. 68GPCh. 40 - Prob. 69GPCh. 40 - Prob. 70GPCh. 40 - Prob. 71GPCh. 40 - Prob. 72GPCh. 40 - Prob. 73GPCh. 40 - Prob. 74GPCh. 40 - Prob. 75GPCh. 40 - Prob. 76GPCh. 40 - Prob. 77GPCh. 40 - Prob. 78GPCh. 40 - Prob. 79GPCh. 40 - Prob. 80GPCh. 40 - Prob. 81GPCh. 40 - Prob. 82GPCh. 40 - Prob. 83GPCh. 40 - Prob. 84GPCh. 40 - Prob. 85GPCh. 40 - Prob. 86GPCh. 40 - Prob. 87GPCh. 40 - Prob. 88GPCh. 40 - Prob. 89GP
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Similar questions
- (b) Copper crystallises as FCC (face centred cubic). Given that the atomic radius and density of a given copper sample are 1.28 x 1010 m and 8.98 x 10' kg/m' respectively, carry out the following: Calculate the mass of the copper sample. T'ake Avogadro's number, NA = 6.023 x 1023 atoms/mole. (i) (ii) If the interatomic planar spacing, d, in the sample above is 2.96 x 1010 m, determine the angle at which the first Bragg reflection will occur from the (111) plane if x-radiation of wavelength 1.52 x 10-10 m is used for the analysis. (c) Give two uses of pure copper and two commercial applications of copper alloys.arrow_forward(b) Copper crystallises as FCC (face centred cubic). Given that the atomic radius and density of a given copper sample are 1.28 x 10-10 m and 8.98 x 10' kg/m' respectively, carry out the following: (i) Calculate the mass of the copper sample. Take Avogadro's number, NA = 6.023 x 1023 atoms/mole. If the interatomic planar spacing, d, in the sample above is 2.96 x 1010 m, determine the angle at which the first Bragg reflection will occur from the (111) plane if x-radiation of wavelength 1.52 x 10-10 m is used for the analysis. (ii)arrow_forwardFor 3D free electron gas, the density of states counts the number of degenerate electron states dn per energy interval dE around a given energy E as g(E): = dn dE 3 (2m₂)2V 1 E2 2π²ħ³ At absolute zero temperature, N electrons can fill up all low lying energy levels (following Pauli exclusion principle) up to a given energy level E called Fermi energy. From the density of states, what is the relation between the total electron states N below a given energy E? Use this result to show that the Fermi energy EF is given by - - 2010 (307² M)³ ħ² 3π²N\3 EF 2me Varrow_forward
- For 3D free electron gas, the density of states counts the number of degenerate electron states dn per energy interval de around a given energy E as g(E) = dn dE 3 (2m₂)²V 1 -E2 2π²ħ³ At absolute zero temperature, N electrons can fill up all low-lying energy levels (following Pauli exclusion principle) up to a given energy level E called Fermi energy. In terms of the Fermi energy, the density of states can now be written as, 3N 263/2 2E g(E) -E¹/2 Using this simplified expression, show that the average energy of an electron in a free-electron gas is given by, 3 (E) = { Ef 1 EF Clue: interpret g(E)/N as probability density for E, and thus (E) = √³ Eg(E)dE NJOarrow_forward(4) Find the Fermi energy of lithium Er, the Fermi temperature TF, and the speed of wF of the fastest free electrons.arrow_forwardJA silicon wafer is doped with 1015 cm 3 donor atoms. Assume light generates density of electrons and holes equal to 1018 cm-3.Calculate the total electron and hole concentrations and location of the quasi-Fermi levels for the electrons and holes with respect to the intrinsic Fermi level. (n = 1x1010 cm-3, Ne = 2.8x1019 cm-3, Ny = 1.04x1019 cm3, T = 300K). %3Darrow_forward
- An atom’s nucleus is a collection of fermions— protons and neutrons. (a) In calculating the Fermi energy in a nucleus, the protons and neutrons must be considered separately. Why? (b) Find the Fermi energy of (i) the protons and (ii) the neutrons in a uranium nucleus, which has a radius of 7.4 x 10-15 m and contains 92 protons and 146 neutrons.arrow_forwardAn n-type Si wafer has been doped uniformly with 10" cm antimony (Sb) atoms. Calculate the position of the Fermi energy with respect to the Fermi energy Er in intrinsic Si nlx10" cm] 0.363 eV 0.288 eV O 0.298 eV O 0.267eVarrow_forwardEstimate the fraction of electrons excite above the Fermi level at room temperature (T=300K) for Sodium and copper? Given the Fermi energy (EF) for sodium and copper is 3.1eV and 7eV respectively.arrow_forward
- Silicon atoms with a concentration of 7× 1010 cm3 are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T=300 K: N. = 4.7 x 1017cm-3 and N, = 7 × 1018cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The hole concentration?arrow_forwardFind the equilibrium electron and hole concentration and the location of the Fermi level for a silicon sample at27∘Cdoped uniformly with5×1015 cm−3phosphorus atoms and4×1015 cm−3boron atoms.arrow_forwardPlot the Fermi function Vs. Energy at the temperature of 500 K, when EF = 2 eVarrow_forward
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