Consider a proton confined within typical nuclear dimensions of 5×10^(−15) m. Estimate the minimum kinetic energy of the proton. Repeat this calculation for an electron confined within typical nuclear dimensions. Comment briefly on the physical significance of your results, given that the nuclear binding energy for a proton is typically in the range 1−10 MeV

In an electron microscope, electrons are used in place of light waves to create images of extremely tiny structures. The electrons are much easier to deal with than the light waves that have similar wavelengths (gamma rays). When the electrons are given the required kinetic energy, their wavelengths will be roughly 0.0037 nm. 24.96.91.88 Use the deBroglie equation to estimate the speed of these electrons. Enter your numerical result below as a multiple of 106 m/s. For example, if you wanted to enter the speed of light you would put the number 300 in the box, because C 3.00 X 108 m/s 300 × 106 m/s. MALUATION

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Suppose that ak > 0 for all k e N and E ak < 0. For each of the following, prove that the given series converges. ak ( a ) ΣΕΙ 1+ k3ak (b) Lk=1 1+ ak Vak (c) Ek=1 k < 0o.

Schrodinger's cat is one of the most common subjects in modern physics for cartoonists. Here's what Erwin Schrodinger said about his famous thought experiment, "One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): In a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if, meanwhile, no atom has decayed. The first atomic decay would have poisoned it. The function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal…

Consider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.

A potential function is shown in the following with incident particles coming from -0 with a total energy E>V2. The constants k are defined as k₁ = 2mE h? h? k₂ = √√2m (E - V₁) h² k3 = √√2m (E - V₂) Assume a special case for which k₂a = 2nπ, n = 1, 2, 3,.... Derive the expression, in terms of the constants, k₁, k2, and k3, for the transmission coefficient. The transmis- sion coefficient is defined as the ratio of the flux of particles in region III to the inci- dent flux in region I. Incident particles E>V₂ I V₁ II V2 III x = 0 x = a

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Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy U(x) = 00 for a O where k is the spring constant. What are the energies of the ground state and fırst excited state? Explain your reasoning. Give the energies in terms of the oscillator frequency wo = Vk/m. Formulas.pdf (Click here-->)