Problem 9.24 If you take the model in Ex. 4.1 at face value, what natural frequencydo you get? Put in the actual numbers. Where, in the electromagnetic spectrum, doesthis lie, assuming the radius of the atom is 0.5 Å? Find the coefficients of refractionand dispersion, and compare them with the measured values for hydrogen at 0°Cand atmospheric pressure: A = 1.36 × 10-4, B = 7.7 x 10-15 m².

To solve this problem, we need to understand a bit about the classical model of an atom in an…

Answered: Problem 9.24 If you take the model in…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Statistical Physics. Microcanonical Ensemble.
Problem 9.22 Calculate the reflection coefficient for light at an air-to-silver inter- face (μ₁ = μ₂ = µ0, €1 = €0,σ = 6 × 107 (2· m)¯¹), at optical frequencies (@ = 4 × 1015/s).
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Problem 1.6.5. A magnetic moment µ in a magnetic field h has energy E+ = Fµh when it is parallel (antiparallel) to the field. Its lowest energy state is when it is aligned with h. probabilities for being parallel or antiparallel given by P(par)/P(antipar) = exp(-E+/T]/ exp[-E-/T] where T is the absolute temperature. Using the fact that the total probability must add up to 1, evaluate the absolute probabilities for the two orientations. Using this show that the average magnetic moment along the field h is m = µ tanh(uh/T) Sketch this as a function of temperature at fixed h. Notice that if h = 0, m vanishes since the moment points up and down with %3D However at any finite temperature, it has a nonzero %3D equal probability. Thus h is the cause of a nonzero m. Calculate the susceptibility, dm lh=0 as a function of T.
1 W:0E *Problem 1.3 Consider the gaussian distribution p(x) = Ae¬^(x-a)² %3D where A, a, and A are positive real constants. (Look up any integrals you need.) (a) Use Equation 1.16 to determine A. (b) Find (x), (x²), and ơ. (c) Sketch the graph of p(x).
Problem 9.20 (a) Show that the skin depth in a poor conductor (σ << we) is (2/0)√√√ε/μ (inde- pendent of frequency). Find the skin depth (in meters) for (pure) water. (Use the static values of ε, μ, and σ; your answers will be valid, then, only at relatively low frequencies.) (b) Show that the skin depth in a good conductor (σ » we) is λ/2л (where λ is the wavelength in the conductor). Find the skin depth (in nanometers) for a typical metal (σ 107 (2 m)¯¹) in the visible range (w≈ 10¹5/s), assuming € ≈ €0 and μ≈μo. Why are metals opaque? (c) Show that in a good conductor the magnetic field lags the electric field by 45°, and find the ratio of their amplitudes. For a numerical example, use the "typical metal" in part (b).
1.7.12 Classically, orbital angular momentum is given by L = r xp, where p is the linear momentum. To go from classical mechanics to quantum mechanics, replace p by the operator -V (Section 14.6). Show that the quantum mechanical angular momentum operator has Cartesian components (in units of h). a ay a Ly=-i(22 -x- az Lx -i a az a əx L₂=-i (x-²) ay
Show complete and explicit solution with step by step explanation. Note: Please don't skip any mathematical algebra.
4.31 If the Earth radiates as a blackbody at an equivalent blackbody temperature TE = 255 K, calculate the radiative equilibrium temperature of the satellite when it is in the Earth's shadow. [Hint: Let dE be the amount of radiation flux imparted to the satellite by the flux density dE received within the infinitesimal element of solid angle dw.] Then, dE = mr-Ido where r is the radius of the satellite and I is the intensity of the radiation emitted by the Earth, i.e., the flux density of blackbody radiation, as given by (4.12), divided by 7. Integrate the above expression over the arc of solid angle subtended by the Earth, as computed in the previous exercise, noting that the radiation is isotropic, to obtain the total energy absorbed by the satellite per unit time Q = 2.21r?oT£ Finally, show that the temperature of the satellite is given by Earth satellite
The example below comes out of griffiths intro to electrodynamics. I was wondering if you can make a spherical and cylindrical problem like this example, one of each and use to divergence theorem to prove both sides of integrals from gauss divergence theorem. Hope this makes sense and thank
Problem 1.17 A particle is represented (at time=0) by the wave function A(a²-x²). if-a ≤ x ≤+a. 0, otherwise. 4(x, 0) = { (a) Determine the normalization constant A. (b) What is the expectation value of x (at time t = 0)? (c) What is the expectation value of p (at time t = 0)? (Note that you cannot get it from p = md(x)/dt. Why not?) (d) Find the expectation value of x². (e) Find the expectation value of p².
Problem 4.25 If electron, radius [4.138] 4πεmc2 What would be the velocity of a point on the "equator" in m /s if it were a classical solid sphere with a given angular momentum of (1/2) h? (The classical electron radius, re, is obtained by assuming that the mass of the electron can be attributed to the energy stored in its electric field with the help of Einstein's formula E = mc2). Does this model make sense? (In fact, the experimentally determined radius of the electron is much smaller than re, making this problem worse).

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