Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 35, Problem 64PP
To determine
The degeneracy of ground state of a quantum dot if it behaves as cubical 3-D square well.
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2. Show that the probability density for the ground-state
solution of the one-dimensional Coulomb potential
energy has its maximum at x = a,.
2. Show that the probability density for the ground-state
solution of the one-dimensional Coulomb potential
energy has its maximum at x =
=ao.
63 O Figure 40-25 is an energy-level di-
agram for a fictitious three-dimensional
infinite potential well that contains one
electron. The number of degenerate
E (/8ml")
14
Triple
states of the levels are indicated: "non"
12
Non
means nondegenerate (which includes the
ground state) and "triple" means 3 states.
If we put a total of 22 electrons in the well,
what multiple of h²18mL? gives the energy
of the ground state of the 22-electron sys-
tem? Assume that the electrostatic forces
between the electrons are negligible.
11
Triple
6.
Triple
Triple
3.
Ground
Figure 40-25
Problem 63.
Chapter 35 Solutions
Essential University Physics
Ch. 35.1 - Prob. 35.1GICh. 35.2 - Prob. 35.2GICh. 35.3 - Prob. 35.3GICh. 35.3 - Prob. 35.4GICh. 35.3 - Prob. 35.5GICh. 35.4 - Prob. 35.6GICh. 35 - Prob. 1FTDCh. 35 - Prob. 2FTDCh. 35 - Prob. 3FTDCh. 35 - Prob. 4FTD
Ch. 35 - Prob. 5FTDCh. 35 - Prob. 6FTDCh. 35 - Prob. 7FTDCh. 35 - What did Einstein mean by his re maxi, loosely...Ch. 35 - Prob. 9FTDCh. 35 - Prob. 11ECh. 35 - Prob. 12ECh. 35 - Prob. 13ECh. 35 - Prob. 14ECh. 35 - Prob. 15ECh. 35 - Prob. 16ECh. 35 - Prob. 17ECh. 35 - Prob. 18ECh. 35 - Prob. 19ECh. 35 - Prob. 20ECh. 35 - Prob. 21ECh. 35 - Prob. 22ECh. 35 - Prob. 23ECh. 35 - Prob. 24ECh. 35 - Prob. 28ECh. 35 - Prob. 29ECh. 35 - Prob. 30ECh. 35 - Prob. 31ECh. 35 - Prob. 32ECh. 35 - Prob. 33ECh. 35 - Prob. 34ECh. 35 - Prob. 35ECh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38PCh. 35 - Prob. 39PCh. 35 - Prob. 40PCh. 35 - Prob. 41PCh. 35 - Prob. 42PCh. 35 - Prob. 43PCh. 35 - Prob. 44PCh. 35 - Prob. 45PCh. 35 - Prob. 46PCh. 35 - Prob. 47PCh. 35 - Prob. 48PCh. 35 - Prob. 49PCh. 35 - Prob. 50PCh. 35 - Prob. 51PCh. 35 - Prob. 52PCh. 35 - Prob. 53PCh. 35 - Prob. 54PCh. 35 - Prob. 55PCh. 35 - Prob. 56PCh. 35 - Prob. 57PCh. 35 - Prob. 58PCh. 35 - Prob. 59PCh. 35 - Prob. 60PCh. 35 - Prob. 61PCh. 35 - Prob. 62PPCh. 35 - Prob. 63PPCh. 35 - Prob. 64PPCh. 35 - Prob. 65PP
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- (a) List all possible sets of quantum numbers (n,l,ml,ms) for the n=3 shell, and determine the number of electrons that can be in the shell and each of its subshells. (b) Show that the number of electrons in the shell equals 2n2and that the number in each subshell is 2(2l+1).arrow_forwardWhich of the following principal levels contains / (angular momentum quantum number) = 3? A. n = 2 level B. both n = 3 and n = 4 levels C. n = 3 level D. n = 4 level How many orbitals are contained in the n = 3 principal number of a given atom? What is the value of the angular momentum quantum number of a d orbital?arrow_forward8. An electron in H atom occupies the state (√eve + R21 a) What is the energy of the electron? b) If you measure the total angular momentum squared (L²), what value(s) you will get and with what probability? c) If you measure the z-component of orbital angular momentum (L₂), what value(s) you might get and with what probability?arrow_forward
- A finite potential well has a potential of 0 between a = 0 and a = L. For an electron, the difference between the ground state and the outside potential is 3 eV. At what distance to the left of the well does the probability density of the electron drop to 0.0001 its value just inside? a. 0.52 nm b. 1.04 nm c. 0.26 nm d. It will never drop to 0.0001 no matter how far you go to the left of the well. e. The probability density is identically zero outside the well. Which statement regarding the well is true? a. The well has infinitely many energy levels. b. For a sufficiently small nonzero outside potential, there won't be any energy levels left. c. No matter how small the nonzero outside potential, there is at least one energy level in the well.arrow_forwardc. n= 2, 1 = 0. 2. Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 3, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.arrow_forwarda. As a multiple of ħ, what is the angular momentum of a d electron? b. What is the maximum z-componet of angular momentum of a d electron? c. Is (L-)max greater than, less than, or equal to L? 2.arrow_forward
- We want to look at the angular momentum structure of one electronic level of an atom. a. The atom has orbital angular momentum L, electron spin angular momentum S and nuclear angular momentum I. For very large magnetic fields B, what are the quantum numbers and energies? b. In addition to the static B field along the z axis, we add a transverse oscillating magnetic field. Which states are now coupled by the oscillating field, i.e. between which states are transitions induced?arrow_forward1. Assume that an electron is trapped in an infinite potential well of the size of an atom (10-10m). a. Compare the probabilities of observing the electron within a width of Ax=1.5x10-11m if the electron is in the fourth excited state n=5 vs. its ground state n=1. b. Compare the energy levels between these two states. c. Calculate the most likely position of the electron and its average position, when its in its fourth excited state n=5.arrow_forward2. An electron is confined to a nanowire 2 nm in length. Model this system as a 1-D particle-in-a-box, going from 0 to 2 nm. a. Compute the probability that the electron is in the range 0.95 ≤ x ≤ 1.05 nm for the states n = 1, 2, 3. b. Compute the probability that the electron is located within a distance of 0.05 nm of the left end of the wire for each of the states n = 1, 10, 100.arrow_forward
- 2. Question 2: a. In your schematic of the hydrogen atom, draw the transition of the electron from the n=1 level to the n=2 level. Label whether the electron gains or loses energy in this transition? 1 b. Find the energy difference between the n=1 level and the n=2 level. Relate this value back to Q1 to make sense of whether the n=1 level or the n=2 level is the lowest energy state. 1/3arrow_forwardWhich of the following lists of quantum numbers for five states of the hydrogen atom are NOT possible? Choose all that apply. a. n = 3, l = 2, ml = -2 b. n = 3, l = 2, ml = 0 c. n = 3, l = 2, ml = 5 d. n = 4, l = -3, ml = 2 e. n = 1, l = 0, ml = 0arrow_forwarda. What is the length of a p electron's angular momentum vector? b. List the possible z components. c. What are the values of the angle that the angular momentum vector makes with the z axis? d. Draw a picture showing all possible orientations of the angular momentum for p electron. 3.arrow_forward
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