Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 35, Problem 62PP
To determine
The degeneracy of first excited state of a quantum dot if it behaves as cubical 3-D square well.
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1. 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.
6. Consider an electron in a hydrogen atom in a state given by
Y(t=0):
√5 {0311(¹,0,9) +20 ³310 (¹, 0,9)}
a. If you measured the energy what values can you get, and what is the probability of
each?
b. Find the expectation value of the L²
c. Find (L) as a function of time.
2. Show that the probability density for the ground-state
solution of the one-dimensional Coulomb potential
energy has its maximum at x = a,.
Chapter 35 Solutions
Essential University Physics (3rd Edition)
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. 10FTDCh. 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. 25ECh. 35 - Prob. 26ECh. 35 - Prob. 27ECh. 35 - Prob. 28ECh. 35 - Prob. 29ECh. 35 - Prob. 30ECh. 35 - Prob. 31ECh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 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. 61PPCh. 35 - Prob. 62PPCh. 35 - Prob. 63PPCh. 35 - Prob. 64PP
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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_forward(a) How many electrons can be in the n=4 shell? (b) What are its subshells, and how many electrons can be in each?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
- Which 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_forward2. Show that the probability density for the ground-state solution of the one-dimensional Coulomb potential energy has its maximum at x = =ao.arrow_forwardWe 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_forward
- 8. 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_forward4. Consider the normal Zeeman effect applied to the 3d to 2p transition. (a) Sketch an energy level diagram that shows the splitting of the 3d and 2p levels when an external magnetic field is applied. Label each state by its magnetic quantum number, mi. (b) State the magnetic quantum number selection rule and sketch the allowed transitions on your diagram. (c) Show that there are only three different transition energies permitted.arrow_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_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_forward1. a. What is the total number of orbitals associated with the principal quantum number n=1? b. What is the total number of orbitals associated with the principal quantum number n=2? c. What is the total number of orbitals associated with the principal quantum number n=3?| d. What conclusion can be drawn from total number of orbitals associated with a given principal quantum number? 2. List the values of n, {, m, for an orbital in the 4d subshell.arrow_forward1. Show that if (ø0) = 0, then (E) is equal to or larger than E = (1|H|1) where E, is the energy of the first excited state. %3D %3D Extend this result to the other excited states.arrow_forward
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