For a system of 2 identical particles with spin 'lI', the ratio of the number of states which are symmetric under spin interchange to the number of states which are anti-symmetric under spin interchange is 3 I+1
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Q: For a system of two identical particles with spin I the ratio of number of states which are…
A: The ratio of the number of states symmetric under spin interchange to the number of states…
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- 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 VProblem 35-28: What is the ground-state energy in electron volts of 10 noninteracting fermions each with a mass of 5.02E-27 kg in a one- dimensional box of length L 3.90E-10 m ? (Because the quantum number associated with spin can have two values, each spatial = state can hold two fermions.) 0.044 eVView a system of two particles that do not interact with each other, where each particle can occupy three possible states, each with energy &, 2ɛ, 3E (i) Marwell-Boltzmann: Na. Configuration 1 2 3 4 S 6 7 2 9 Nader Conligation 1 2 2 + 1 2 5 6 (1) Fermi-Dirac 3 No. Configuration E AG A A B B AA A A Distinguishable 28 E AB (6) Boson: Base- Ginstein: Indistinguishable င် A A B A A 8 28 AA A A 38 A 2 A AB B A CO B A JE AA A A Energy system A A wwwww Indistinguishable We know formion follow exclusion principle. 28 38 Smarty tem 28 32 38 4E SE SE Energy system 22 48 68 38 48 SE 38 4€ SE Calculate the average energy of the system as a temperature function for the three statistics above.
- Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it-that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13×10−10m and the dissociation energy is 1.54×10−18J per molecule. Find the value of the constant a. Find the value of the constant b.P9E.11 (a) For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies E, of the resulting A molecular orbitals are given by: E, =a+2B cos- N+1 k=1, 2,.,N Use this expression to make a reasonable empirical estimate of the resonance integral B for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene given that t-n ultraviolet absorptions from the HOMO to the LUMO occur at 61 500, 46 080, 39 750, and 32 900 cm", respectively. (b) Calculate the T-electron delocalization energy, Egdo:= E, - n(a+ B), of octatetraene, where E, is the total T-electron binding energy and n is the total number of T-electrons. (c) In the context of this Hückel model, the molecular orbitals are written as linear combinations of the carbon 2p orbitals. The coefficient of the jth atomic orbital in the kth molecular orbital is given by: cN sin j=1,2.N jkn j=1, 2,.,N Evaluate the coefficients of each of the six 2p orbitals in each…5.47 Germanium is doped with 5 × 10¹5 donor atoms per cm³ at T = 300 K. The dimen- sions of the Hall device are d = 5 x 10-³ cm, W = 2 × 10-² cm, and L = 10-¹ cm. The current is I = 250 μA, the applied voltage is V. = 100 mV, and the magnetic flux density is B₂ = 500 gauss = 5 x 10-2 tesla. Calculate: (a) the Hall voltage, (b) the Hall field, and (c) the carrier mobility.