A free electron has a kinetic energy 14.8eV and is incident on a potential energy barrier of U = 34.7 eV and width w =0.061nm. What is the probability for the electron to penetrate this barrier (in %)? ou Answered 1.24 orrect Answer 6.1533 margin of error +/- 1%
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- We can approximate an electron moving in a nanowire (a small, thin wire) as a one-dimensional infi nite square-well potential. Let the wire be 2.0 μm long. The nanowire is cooled to a temperature of 13 K, and we assume the electron’s average kinetic energy is that of gas molecules at this temperature ( 3kT/2). (a) What are the three lowest possible energy levels of the electrons? (b) What is the approximate quantum number of electrons moving in the wire?What constraints does the uncertainty principle place on our knowledge of the world? To get a sense of scale, we’ll look at the uncertainty in speed for a confined electron and for a confined dust particle.a. What range of velocities might an electron have if confined toa 0.30-nm-wide region, about the size of an atom?b. A 1.0@mm@diameter dust particle (m ≈ 10-15 kg) is confined within a 5-μm-long box. Can we know with certainty if the particle is at rest? If not, within what range is its velocity likely to be found?An electron in a one-dimensional infinite potential well of length L has ground-state energy E1.The length is changed to L' so that the new ground-state energy is E'1 = 0.500E1 .What is the ratio L'/L?
- 6. An electron in hydrogen atom is in initial state Þ(r, 0) = A(2410o + iÞ210 + 421–1 – 2ib211) where wnim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? hw = - n2 c. Write the state Þ(r, t) at time t, using energy eigenvalues as En d. Find the expectation value of L in the state Þ(r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of Lz led to the value –ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities?a. Calculate the minimum uncertainty in the position of an electron in meters, if its velocity has been measured to within 2.34e-06 m/s. For the mass of an electron use 9.10938356 × 10-31 kg and for huse 1.0545718 x 10-34 Js. m b. 44 = 141² = ² represents a: O the pitchfork operator O probability density O numerov program O wave function c. The sum of all the little bits of probability over possible measurements that can be made (i.e. over all space): S4²4 = 1 is called: O the quantum condition O the normalization condition O the human condition O the eignen condition(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 m, what is the electron's minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?
- The probability of finding a particle moves in the left quarter of a one-dimensional box of length a for energy level n =2 is: A. 15% В. 20% C. 25% D. 35% E. 50% A C B C c C D C E CA quantum system has a ground state with energy Eo = 0 meV and a 2-fold degenerate excited state with energy E₁ = 50 meV. E1 Calculate the probability of finding the system in its ground state when it is at T = 300 K. Select one: O a. 0.78 O b. 0.22 O c. 1 O d. 0.87C. For a particle of mass 9.10938356×10-31 kg scooting back and forth on a wire of length 13×10-10 m, compute it's energy in the n = 9 state. Use: π = 3.14159265359 and h = 1.0545718×10-34 Js. Eg J. D. What is the rule for the number of nodes for a particle-in-a-box state as a function of its quantum number? Number of nodes = On ΟΙ O n-1 On--1
- If the position of an electron in a membrane is measured to an accuracy of 3.58 µm, what is the electron's minimum uncertainty in velocity (in m/s)? a) If the electron has this velocity, what is its kinetic energy in eV? b) What are the implications of this energy, comparing it to typical molecular binding energies?An electron trap in an infinite potential Well length 2.0o nm Electron Can be considered as free particle - having particle and 4(x)=Asin UIS > x>0 品) 11 UIS 7. 11 X. xp find the probabiliy of Kinetic energy between 77x>O Schro the x >0 umop nger uation for the electron in infante potential wellA quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4ϵ, 9ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ =0.035 eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature is
