5. Starting from the definition of chemical potential for multi-components, please derive hat G'(P, T, N)-Σ μ(P, T, N) N 5. Starting from the definition of chemical potential for multi-co...
1. Infinite potential quantum well. (1) Starting from the Schrödinger equation, please derive the quantized energy levels and wave functions for an infinite potential quantum well of width D 2 nm. (2) Photon emission wavelength: Please calculate the emitted photon wavelength if an electron falls from the n-2 state into n-l state inside this infinite potential quantum well. (3) Heisenberg uncertainty principle: For the n-2 state of an electron inside an infinite potential well, prove that the Heisenberg uncertainty relation...
Derive expressions for a Fermi gas in 2-D box of area A for the following: (a) The Fermi energy aSEF-n2/(4πm) (N/A). (b) The T-O energy as U-1/2 N EF (c) Density of states g(e) N/EF (d) Solve N-J g(ε) nFD(ε)de (where the integral goes from 0 to 00) for the chemical potential, μ(T), and show that the chemical potential recovers kT>XE (classical) and kT<< ε,degenerate Fermi gas) limits. Derive expressions for a Fermi gas in 2-D box of area A...
Please explain very carefully! 4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 > 0 are unknown. (a) (5 marks) Let μ+σ~p denote the p-th quantile of the N(μ, σ*) distribution. What does this mean? (b) (10 marks) Determine a UMVU estimate of,1+ ơZp and justify your answer. 4. Suppose that x = (x1, r.) is a sample from a N(μ, σ2) distribution where μ E R, σ2 >...
please explain this qustion. Let X ∼N(1,4) and g(t) = P(X > t), −∞< t <∞. (a) Find the value t that minimizes g(t+4)−g(t) and justify your answer. (b) Redo (a) for X ∼N(1,σ2). Does your answer depend on σ? Explain why.
5. (9 marks) Derive an expression for the equilibrium constant starting from: G = G°+RTIN
5. (worth 16 points) Consider a test of H : μ-65 versus Ha μ > 65. The test uses σ-10, α-01 size of n 64. and a sample a. Describe the sampling distribution of Fassuming Ho is true. Mean (t)- Standard deviation (oz)- Shape: Sketch the sampling distribution of x assuming Ho is true is used as the test stat istic. Locate the rejection region on your graph from b. Specify the rejection region when x part a. C. Describe...
please do the full working everyone is just jumping to the answer im trying to understand the working please Light consists of photons: noninteracting quantum oscillator particles with an energy E-hv- e, where is their frequency, A is their wavelength, and c is their speed (ie the speed of light) The momentum of a photon, p has a special definition, because photons have no mass. We instead use the De Broglie identity p-. This means that we can relate the...
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...
This is physical chemistry problem from Atkins 5. [20 (1) The variation of chemical potential, u of a perfect gas with pressure can be expressed as follows: Au RT ln Derive the below equation for Gibbs energy of mixing, when two gases of A and B are mixed at constant pressure, p and temperature, T. (2) Calculate the molar Gibbs energy of mixing when the two major components of air (nitrogen and oxygen) are mixed to form air at 298...
Let X be binomial with parameters n and p. Evaluate E{X(X − 1)} from first principles (i.e. the definition of expectation), and hence, derive var(X). You may assume linearity of expectation, and that E(X) = np.