MODERN PHYSICS (LOOSELEAF)
4th Edition
ISBN: 9781119495550
Author: Krane
Publisher: WILEY
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Chapter 5, Problem 5P
To determine
The three smallest energy values of the electron.
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An electron is trapped in a one-dimensional region of width 0,05 nm. Find the three smallest possible values allowed for the energy of the electron.
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An electron is trapped in a one-dimensional region
of length 1.00 x 10-10 m (a typical atomic diameter).
(a) Find the energies of the ground state and first two
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ond excited state? (c) From the second excited state, the
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MODERN PHYSICS (LOOSELEAF)
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- A certain atom requires 3.0 eV of energy to excite an electron from the ground level to the first excited level. Model the atom as an electron in a box and find the width L of the box.arrow_forwardA proton is confined to a nucleus whose diameter is 5.5 × 10^−15 ?. If this distance is considered to be the uncertainty in the position of the proton, what is the minimum uncertainty in its momentum?arrow_forwardAn electron is confined to a region of space of length 0.19 nm— comparable in size to an atom. What are the first three allowed energies of the electron?arrow_forward
- A particle of mass m is confined to a 3-dimensional box that has sides Lx,=L Ly=2L, and Lz=3L. a) Determine the sets of quantum numbers n_x, n_y, and n_z that correspond to the lowest 10 energy levels of this box.arrow_forwardA rectangular corral of widths Lx = L and Ly = 2L holds an electron.What multiple of h2/8mL2, where m is the electron mass, gives (a) the energy of the electron’s ground state, (b) the energy of its first excited state, (c) the energy of its lowest degenerate states, and (d) the difference between the energies of its second and third excited states?arrow_forwardDetermine the mean radius for the 2s electron.arrow_forward
- A relatively long-lived excited state of an atom has a lifetime of 3.00 ms. What is the minimum uncertainty in its energy?arrow_forwardA cubical box of widths Lx = Ly = Lz = L contains an electron.What multiple of h2/8mL2, where m is the electron mass, is (a) the energy of the electron’s ground state, (b) the energy of its second excited state, and (c) the difference between the energies of its second and third excited states? How many degenerate states have the energy of (d) the first excited state and (e) the fifth excited state?arrow_forwardA proton is trapped in a one-dimensional box of length L. If the zero-point energy is to be 71.0 eV, what is L?arrow_forward
- An electron is bound in a square well of width 1.50 nm and depth U0 = 6E1-IDW. If the electron is initially in the ground level and absorbs a photon, what maximum wavelength can the photon have and still liberate the electron from the well?arrow_forwardAn electron is in a three-dimensional box. The xx- and zz-sides of the box have the same length, but the yy-side has a different length. The two lowest energy levels are 2.18 eVeV and 3.47 eVeV, and the degeneracy of each of these levels (including the degeneracy due to the electron spin) is two. What is the length LY for side of the box? What are the lengths LXLX, LZLZ for sides of the box? What is the energy for the next higher energy state? What are the quantum numbers for the next higher energy state? What is the degeneracy (including the spin degeneracy) for the next higher energy state?arrow_forwardA photon with wavelength 8.00 nm is absorbed when an electron in a three-dimensional cubical box makes a transition from the ground state to the second excited state. What is the side length L of the box?arrow_forward
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