(a) Count the number of electron states N(E) with energy equal to or less than E in Equation 35.8 by finding the volume available to such states in the space with Cartesian coordinate axes nx, ny, nz. (Hint: Consider each set of positive integers, at the corner of a unit cube, and that lies inside a radius
Want to see the full answer?
Check out a sample textbook solutionChapter 37 Solutions
Essential University Physics: Volume 2 (3rd Edition)
- For a material having FCC crystal cell structure, write the expressions for Planar atomic density in planes (0,0,1) and (1,1,0) in terms of atomic radius ‘r’ and calculate for Copper in gms/cm3 . Why metal shows directional nature of properties at atomic level whereas its bulk measured properties are isotropic in nature.arrow_forwardCalculate the radius of a nickel atom in cm, given that Ni has an FCC crystal structure, a density of 7.982 g/cm³, and an atomic weight of 58.69 g/mol.arrow_forwardLall space Jall space 6. Self energy of a sphere of radius R and and uniform charge density with total charge Q is[Assume energy is given by U = where dt is elemental volume] 3 Q? Q r)² (4=r²dr) + /, o -)² (4#r² dr) = 1 R 1 Q 2 (True, False) = Lll space 2 €0 E²dr U = 4περτ2 5 4T€0 R 2 4περ R3arrow_forward
- 6c.2. The integrate the electron density n is the integral of the density state using the 2D density of states and the Fermi-Dirac distribution, EF = [ƒ¥D(E) · 9(E) de · n = Fermi - Dirac distribution density of state in 2D per unit area → fFD(E): = g²D (E) 1 eß(ε-μ) + 1 1 dN (2D) A dE To show that the chemical potential of a Fermi gas in two dimensions is, H(T) = k¸T \n [exp (™ 47 In [exp (m²) - 1] mkgT || mº πηarrow_forwardTin (Sn) has a superconductive critical temperature Tc = 3.7 K and critical magnetic field at T = 0 K equal to Bc = 31 mT. What is the maximum magnetic field Sn can sustain at the critical temperature without losing its superconducting state? What is the minimum radius required for an infinite linear wire of Sn if it is to carry a current of 200 A at T = 3.0 K whilst still in its superconducting state?arrow_forwardDraw diagrams to scale, and similar to Fig. 7F.7a, representing the states (i) l = 0, (ii) l = 3 and all possible values of ml.arrow_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. 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_forwardQUESTION 1: Hydrogen atom in a general state (ignoring spin): The orthonormal energy eigenstates of the hydrogen atom n,,m are labelled by the principal quantum number n and the orbital angular momentum quantum numbers I and m. In the following you may write the energy eigenvalues as En E. The state of a hydrogen atom at time t = 0 is given by a linear combination of energy eigenstates V (√561,0,0 — √342,1,1 + i√3,2,-2) · (a) Write down the wave function for later times t> 0 assuming the atom is undisturbed. (b) Show that this state is correctly normalised. (c) Find the expectation values of the energy and Îz if the system is in the state V. 2² Hint: No integrations needed, just use the known eigenvalues of Un,1,m with respect to and write the energy eigenvalues as En = ₁. n². = and Îz,arrow_forwardsolve it completely. What are the additional assumption made in the shell model ? Discuss the possible cause for (a) the difference in the energy of j+1/2 and j-1/2 states (b) the pairing energy.arrow_forward
- Estimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following: (a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.) (b) Would you expect the rotational energy levels of diatomic molecules to be excited at room temperature? (It costs about 10-4 eV to promote such a system to an excited rotational energy level.)arrow_forwardTaking into account electron spin, what is the total number of states with n=3?arrow_forwardEstimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following: (a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.) (b) Would you expect the rotational energy levels of diatomic molecules to be excited at room temperature? (It costs about 10−4 eV to promote such a system to an excited rotational energy level.)arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON