and a at cm at 855K for a sample composed of these atoms. Hint: You will need to calculate the molecular partition Calculate the electronic contribution to the molar internal energy Hint 2: Remember that Rs = bo T
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- Q:: A Si sample is doped with 107 cm3 As. What is the equilibrium hole concentration at 300 k? and where is Ep relative to E,? Take n = 1.5 x 1010 cm-. (Ans. 2.25 x 10'cm,0.407ev).A system with 3 (three) indistinguishable particles has five energy states: E1 = 0, E2 = E, E3 = 2E, E4 = 3E, Es = 4E. Determine the possible formation if it satisfies: a. Fermi Direct Statistics?1. Pressure and bulk modules of an electron gas. (a) Derive a relation connecting the 3 pressure and volume of an electron gas at OK. Hint: Use the result of U == the relation between & and electron concentration. The result may be written as 200 3V 5p B = = p= 10U 3 9V of the electron gas contribution to B. NE N&F and . др (b) Show that the bulk modules B = -V. of an electron gas at OK is av . 5 (c) Estimate for potassium, using Table 1 of the textbook, the value
- Suppose we have an ideal fermion gas of identical particles in a "box" at T = 0 K. Which of the following statements are true? a. The multiplicity of the gas is =1 b. The multiplicity of the gas is =N! C. If the gas consists of electrons with densities that correspond to the typical densities of conduction electrons in metals, only a part of the electrons can contribute to the heat capacity of the system as the temperature rises. d. If the gas consists of electrons with densities corresponding the typical densities of conduction electrons in metals, all electrons can easily contribute to the heat capacity of the system as the temperature rises.2) An atomic nucleus can be crudely modeled as a gas of nucleons with a number density of 0.09 fm-3 (where 1 fm = 10-15m). a) Calculate the Fermi energy ɛp of this system. b) Also, calculate the Fermi temperature TF. Is it reasonable to treat the nucleus as a degenerate Fermi gas at room temperature? c) Calculate the degeneracy pressure of the nucleus. What keeps the nucleus from blowing apart due to this degeneracy pressure?The Boltzmann constant has a value of kg = 0.69503476 cm-1/K. At what temperature would kBT be equivalent to the first energy level spacing, E₁-Eo ha for a harmonic oscillator of frequency w = 500 cm-1? This is a crude indication of the temperature needed to appreciably populate the n = 1 vibrational level. =
- uestion 9 ot yet swered Carbon tetrabromide, initially at standard atmospheric pressure is now stored in a container at 5.17x10 Pa. If density of CCI, is 3.42 g/cm, then its pressure energy is equal to J/kg. arked out of O 1511.69x106 Flag question O 1.482 x106 O 1511.69 O 1482.061. Compute the partition function Z¡(T, V, N, B) of a single molecule as a function of the temperature T, volume V, the number of molecules N, and the magnetic field B. 2. What are the probabilities for S of a specific molecule to take the values +1 and – 1 at temperature T? 3. Find the pressure P of the gas as a function of T, V, N, B. How the pressure behaves as you flip the direction of the magnetic field?In discussing molecular rotation, the quantum num- ber J is used rather than 7. Using the Boltzmann distribution, calculate nj/no for ¹H³5Cl for J = 0, 5, 10, and 20 at T = 1025 K. Does ny/no go through a maximum as J increases? If so, what can you say about the value of J corre- sponding to the maximum?
- Q1:-Show that r2 for a spherical Fermi distribution, p(r) = Po|1+exp ( be expanded in () according to the expression: , can r? =R|1 + +-| 7n2 + .. Q2:- As nuclear model, the nucleus may separated into core and skin. Assume the core is uniformly charged with constant density Po, and the skin charge is linearly fall off to zero at the surface over 90% of the radius Ro. Calculate the electron scattering form factor F(q)from this model.A:08 الرسائل المحفو. . . 1 03: Rhenium has a Hexagonal Close-Packed crystal structure with an atomic radius of 0.137 nm and a ratio c/a of 1.615, compute: a) The volume of the unit cell. b) The theoretical density c) Atomic packing factor Note: Avogadro's' number = 6.023×10²³ Atomic weight = 186.21 g/mol إضافة وصف.. . IIIProblem 1 Consider a molecular two-level system with a twofold degenerate ground state (la- beled “0") and a threefold degenerate level (labeled “1") with an energy (expressed in wavenumbers) 150.0 cm-1 above the ground state. (a) What is the proportion N1/N of molecules in the higher level at T = 400 K? (b) What is the molecular average energy (relative to the ground state and expressed in wavenumbers) when the temperature is T = 400 K? (c) What is the proportion No/N of molecules in the ground state when T → 0K? (d) What is the proportion N1/N of molecules in the higher level when T →?