Answer Happy

QUANTUM PHYSICS QUESTION PLEASE HELP
QUESTION 2 The attractive electrostatic potential energy between free electrons and metal lattice ions can be approximated by PE = (-2.3)k Ve 2 p¹/3, where: ke-is Coulomb's constant V-volume p-N/V (N is electron number) e-electron charge Consider the electrons as an ideal Fermi gas at OK, and call the Fermi energy &. The kinetic energy of this gas and the electron density in terms of the Fermi surface are given in your notes. The expression for the total energy of the gas now has a potential energy term as well, and can be written as Etat = (3/5)N&+PE. 2.1. Consider a metal with a fixed number of electrons. Its equilibrium volume V (the point where the energy is minimised w.r.t. V) is given by: [9] a) V = b) V = (3m²)²/33N¹/3h² 5x2.3x6²kçm e) V = f) V= [(3m²)²/³3N¹/³h² e²kçm c) V = d) V = 0 [(3m²)²/³¹/³²1¹ e²kçm -- [15] 1/3 (3m²)2/33N1/321/3 5x2.3xe²kçm [(3m²)2/33N¹/3h²³ 5x2.3x6² kcm a) 0.74 x 10 moles b) 0.74 x 10 moles 2.2. The expression for the volume can be written in terms of the Bohr radius a as V=N (2.47 a)³ If the Bohr radius is a = 5.29 x 10¹¹ m, how many moles of electrons does this model predict there to be per cubic meter of metal? (Avogadro's number: 6.02x10²) [6] c) 0.41 x 10 moles d) 0.12 x 10° moles e) 0.12 moles f) 0.74 moles