An electron is trapped in a 3D cube of side length 2 nanometers centered at the origin (x, y, and z all can be between -1nm and 1 nm). What points in space would the probability distribution function be at a maxima if Nx = 1, Ny = 2, and Nz = 1?
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An electron is trapped in a 3D cube of side length 2 nanometers centered at the...
Consider a quantum particle in a 3D box that is not a cube. It has side lengths: a = 1 Å b = 1 Å c = 2 Å Answer the following: 1. Derive the wave vector k in the terms of nx, ny, and nz 2. find the equation for energy as a function of nx, ny, and nz 3. List the five lowest energies a particle can have in this system and list all the different states for...
Integrate A=(sinx, yx, cosz) over the outer surface of a cube with side length 1. For simplicity, place one vertex of the cube at the origin and align its three neighboring edges along the positive x, y, z axis, respectively. For each face of the cube, calculate A•n before doing the integration, where n is the norm of that face (the unit vector perpendicular to the surface that points outward).
Page Two Consider an electron trapped in a 1-D box of length 5.0 nm, and we have determined that the probability of finding the electron in a particular state is represented by the following illustration. Answer the questions below: |Y12 - - - - - - - - - - ЛР - - 5 nm X 1. What is the value of the quantum number in this state? 2. What is the energy of the electron in this state where...
1. (3 points) A charge is at the center of a cube of side length a . What is the electric flux through the cube due to this charge? 2. (3 points) A charge Q is a distance b above the center of the top face of a cube of side length a. (Note: This charge is outside of the cube.) What is the electric flux through the cube due to this charge? 3. (4 points) A parallel plate capacitor...
(8pts.) Let random variable X be the length of a side of a square. Suppose that X has the probability density function, f(x) = 1 / 2 0 < 252. (a) Find P(X < 0.5). (b) What is the variance of X? (C) Let Y be the volume of a cube built with the length of each side being X. Note that Y = X3. What is the expected volume of the cube, E(Y)?
The Problem: Depress the equation r6r +100 1. Decomposing a cube: Consider a cube with side length (a) Suppose we break the side of the cube at an arbitrary point ryb. This cut triggers the decomposition of the cube into the 8 pieces you have with your manipulative. You will have a cube with side length y and a cube with side length b. Identify the other 6 solids in terms of their dimensions using y and b so that...
Reserve Problems Chapter 5 Section 7 Problem 1 Suppose that the length of a side of a cube X is uniformly distributed in the Interval 9<x< 10. Determine the probability density function of the volume of the cube Express your answers in terms of v. Edie for v € (99, 10), v (v) - 2 forv * vC (9.10'). westion with no attempts available to Show Work for this question Open Show Work
2. Electron overlap with nucleus (very important for electron capture): Since the possible position of the electron is smudged out, it even may overlap with the nucleus. a) What is the probability of an electron in the (1,0,0) state being between r-0 and ao? b) What is the probability of an electron in the (1,0,0) state being between r-0 and 1.25 fm? (remember how to solve integrals for a very small interval, see example 5.3) Example 5.3 Consider again an...
roblem 4 points A point A (X, Y, Z) in a three-dimensional Euclidean space R3 has the uniform joint distribution within the ball of radius 1 centered at the origin (OinR3.) Consider a random variable, T d (A, O), that is the distance from A to the origin. 1. Find the cumulative distribution function for T 2. Evaluate its expectation, E T] 3. Evaluate the variance, Var [T] .
Situation 1: You have a metal cube, measuring L on each side. The metal is in electrostatic equilibrium and has a net 4. charge of Q,. The cube has a cavity within it, however-where there is no metal. The shape of this cavity is not known. Somewhere within the cavity rests a point charge, q,. Its exact location is unknown, but it is not in contact with the inner wall of the cavity At a certain point P, on the...