Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 41, Problem 17P
(a)
To determine
To show that the given wave function is normalized.
(b)
To determine
The probability of the electron.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The wave function for the Is state of an electron in the hydrogen
atom is
VIs(P) =
e-p/ao
where ao is the Bohr radius. The probability of finding the electron in
a region W of R³ is equal to
J, P(x, y, 2) dV
where, in spherical coordinates,
p(p) = |V1s(P)²
Use integration in spherical coordinates to show that the probability of
finding the electron at a distance greater than the Bohr radius is equal to
5/e = 0.677. (The Bohr radius is ao =5.3 x 10-1" m, but this value
is not needed.)
The probability density function (PDF) for electrons to be detected on the x-axis
between 0 nm and 1.0 nm is shown below.
What is the probability of finding the electron between x = 0.5 nm and x =
1.0 nm?
|w(x)* (nm')
2.0
1.0
0.5
x (nm)
1.0
The total probability of finding an electron in the hydrogen atom is related to the integral
∫ r2 e-2r/ao dr
Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.
Chapter 41 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 41.3 - Prob. 41.1QQCh. 41.3 - Prob. 41.2QQCh. 41.4 - Prob. 41.3QQCh. 41.4 - Prob. 41.4QQCh. 41.8 - Prob. 41.5QQCh. 41 - Prob. 1PCh. 41 - Prob. 2PCh. 41 - Prob. 3PCh. 41 - Prob. 4PCh. 41 - Prob. 5P
Ch. 41 - Prob. 6PCh. 41 - Prob. 7PCh. 41 - Prob. 8PCh. 41 - Prob. 9PCh. 41 - Prob. 10PCh. 41 - Prob. 11PCh. 41 - Prob. 13PCh. 41 - Prob. 14PCh. 41 - Prob. 15PCh. 41 - Prob. 16PCh. 41 - Prob. 17PCh. 41 - Prob. 18PCh. 41 - Prob. 19PCh. 41 - Prob. 20PCh. 41 - Prob. 21PCh. 41 - Prob. 23PCh. 41 - Prob. 24PCh. 41 - Prob. 25PCh. 41 - Prob. 26PCh. 41 - Prob. 27PCh. 41 - Prob. 28PCh. 41 - Prob. 29PCh. 41 - Prob. 30PCh. 41 - Prob. 31PCh. 41 - Prob. 32PCh. 41 - Prob. 33PCh. 41 - Prob. 34PCh. 41 - Prob. 35PCh. 41 - Prob. 36PCh. 41 - Prob. 37APCh. 41 - Prob. 39APCh. 41 - Prob. 40APCh. 41 - Prob. 41APCh. 41 - Prob. 42APCh. 41 - Prob. 44APCh. 41 - Prob. 45APCh. 41 - Prob. 46APCh. 41 - Prob. 47APCh. 41 - Prob. 49APCh. 41 - Prob. 50APCh. 41 - Prob. 51CPCh. 41 - Prob. 52CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Consider the sp hybrid orbital of the H-atom: |spx-> =. 1 -(|2s > - |2p,>) (a) Find the expectation value of Lz in the |spx-> state in units of h. That is, find: /ħarrow_forwardthe probability of an electron in the ground state of thehydrogen atom being at a distance r from the center of the atom isP1s(r) = 4r2a30e−2r/a0 r = a0, is the value of r that has the greatest probability. Prove thisarrow_forwardConsider the electron in a hydrogen atom is in a state of ψ(r) = (x + y + 3z)f(r).where f(r) is an unknown function depending only on r.(a) Is ψ an eigenstate of Lˆ2? Find the eigenvalue if your answer is ’Yes’.(b) Compute the probabilities of finding this electron in eigen states with m = −1, 0, +1. (c) Compute <Lz> in this state.arrow_forward
- An electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?arrow_forwardA spin state of an electron in the vector form is given by 3i X = A 4 %3D (a) Determine the normalization constant A, assuming it to be real and positive. (b) Write down the x using the X+ and X-. If z-component of the spin of the electron is measured, what is the probability of finding the value in +ħ/2? (c) Determine the expectation value and uncertainty of S? in terms of h when the electron is in spin state x. Justify your answer. (d) Determine the expectation value of the product S?S, in terms of h when the electron is in spin state X.arrow_forwardAn electron is in a 3p state in the hydrogen atom, given that the expectation value is 12.5a_0 What is the probability of finding the electron within +/- a_0 of your expectation value. (That is, in the range (r − a_0) < r < (r+a_0) where r is the expectation value from above. The answer should be 0.1991.arrow_forward
- We are going to use Heisenberg's uncertainty principle to estimate the ground- state energy of hydrogen. In our model, the electron is confined in a one- dimensional well with a length about the size of hydrogen, so that Ax = 0.0529 nm. Estimate Ap, and then assume that the ground-state energy is roughly Ap2/2me. (Give your answer in Joules or electron-volts.)arrow_forwardFor what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.0 mm? Assume that l has its maximum value of n - 1.arrow_forwardThe average value (or expected value) of r^k, where r is the distance of an electron in the state with principal quantum number n and orbital quantum number leo proton in the hydrogen atom is given by the integral below, where Pnl(r) is a radial probability density of the state with quantum number n, lek is an arbitrary power. For an electron in the ground state of the hydrogen atom. a) calculate <r>nl in terms of the Bohr radius aB b) calculate <l/r>nl in terms of aB c) calculate <U(r)>nl, where U(r) = -e^2/(4piE0r). Respond in eV units. d) Considering also that the electron is in the ground state, estimate the expected value for two kinetic energy <K> and its mean quadratic velocity v. e) Is it justifiable to disregard relativistic corrections for this system? Justify.arrow_forward
- Chapter 38, Problem 071 For the arrangement of Figure (a) and Figure (b), electrons in the incident beam in region 1 have energy E has a height of U1 = 823 ev and the potential step = 617 ev. What is the angular wave number in (a) region 1 and (b) region 2? (c) What is the reflection coefficient? (d) If the incident beam sends 5.29 x 105 electrons against the potential step, approximately how many will be reflected? V= 0 V< 0 x = 0 region 1 region 2 (a) Energy --E- Electron (b)arrow_forwardFor a "particle in a box" of length, L, the wavelength for the nth level is given by An 2L %3D 2п and the wave function is n(x) = A sin (x) = A sin (x). The energy levels are пп %3D n?h? given by En : %3D 8mL2 lPn(x)|2 is the probability of finding the particle at position x in the box. Since the particle must be somewhere in the box, the integral of this function over the length of the box must be equal to 1. This is the normalization condition and ensuring that this is the case is called “normalizing" the wave function. Find the value of A the amplitude of the wave function, that normalizes it. Write the normalized wave function for the nth state of the particle in a box.arrow_forwardThe time-independent w (r) = √ 1 P = wavefunction of the ground state of the hydrogen electron is a function of radial position r. y 3/2 elas In the equation, ao 0.0529 nm is the Bohr radius. What is the probability P of finding the hydrogen electron within a spherical shell of inner radius 0.00600 nm and outer radius 0.0316 nm?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning