Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 35, Problem 63PP
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 =
=ao.
2. Show that the probability density for the ground-state
solution of the one-dimensional Coulomb potential
energy has its maximum at x = a,.
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?
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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- 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.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_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
- c. 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 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. 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_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_forward2. 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_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
- a. 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_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_forward6. 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.arrow_forward
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