University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 40, Problem 40.40E
(a)
To determine
The ratio of
(b)
To determine
The ratio of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Consider the wave function
y(0,0) = 3 sin cos 0e -2(1-cos²0)²
(a) Write y(0,0) in terms of the spherical harmonics.
(b) Write the expression found in part (a) in terms of the Cartesian coordinates.
(c) Is (0,0) an eigenstate of 2 or î?
(d) Find the probability of measuring 2ħ for the z-component of the orbital angular
momentum.
For 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.
The radii of atomic nuclei are of the order of 5.0 * 10-15 m. (a) Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus. (b) Take this uncertainty in momentum to be an estimate of the mag- nitude of the momentum. Use the relativistic relationship between energy and momentum, Eq. (37.39), to obtain an estimate of the ki- netic energy of a proton confined within a nucleus. (c) For a proton to remain bound within a nucleus, what must the magnitude of the (negative) potential energy for a proton be within the nucleus? Give your answer in eV and in MeV. Compare to the potential energy for an electron in a hydrogen atom, which has a magnitude of a few tens of eV. (This shows why the interaction that binds the nucleus together is called the “strong nuclear force.”)
Chapter 40 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 40.1 - Does a wave packet given by Eq. (40.19) represent...Ch. 40.2 - Prob. 40.2TYUCh. 40.3 - Prob. 40.3TYUCh. 40.4 - Prob. 40.4TYUCh. 40.5 - Prob. 40.5TYUCh. 40.6 - Prob. 40.6TYUCh. 40 - Prob. 40.1DQCh. 40 - Prob. 40.2DQCh. 40 - Prob. 40.3DQCh. 40 - Prob. 40.4DQ
Ch. 40 - If a panicle is in a stationary state, does that...Ch. 40 - Prob. 40.6DQCh. 40 - Prob. 40.7DQCh. 40 - Prob. 40.8DQCh. 40 - Prob. 40.9DQCh. 40 - Prob. 40.10DQCh. 40 - Prob. 40.11DQCh. 40 - Prob. 40.12DQCh. 40 - Prob. 40.13DQCh. 40 - Prob. 40.14DQCh. 40 - Prob. 40.15DQCh. 40 - Prob. 40.16DQCh. 40 - Prob. 40.17DQCh. 40 - Prob. 40.18DQCh. 40 - Prob. 40.19DQCh. 40 - Prob. 40.20DQCh. 40 - Prob. 40.21DQCh. 40 - Prob. 40.22DQCh. 40 - Prob. 40.23DQCh. 40 - Prob. 40.24DQCh. 40 - Prob. 40.25DQCh. 40 - Prob. 40.26DQCh. 40 - Prob. 40.27DQCh. 40 - Prob. 40.1ECh. 40 - Prob. 40.2ECh. 40 - Prob. 40.3ECh. 40 - Prob. 40.4ECh. 40 - Prob. 40.5ECh. 40 - Prob. 40.6ECh. 40 - Prob. 40.7ECh. 40 - Prob. 40.8ECh. 40 - Prob. 40.9ECh. 40 - Prob. 40.10ECh. 40 - Prob. 40.11ECh. 40 - Prob. 40.12ECh. 40 - Prob. 40.13ECh. 40 - Prob. 40.14ECh. 40 - Prob. 40.15ECh. 40 - Prob. 40.16ECh. 40 - Prob. 40.17ECh. 40 - Prob. 40.18ECh. 40 - Prob. 40.19ECh. 40 - Prob. 40.20ECh. 40 - Prob. 40.21ECh. 40 - Prob. 40.22ECh. 40 - Prob. 40.23ECh. 40 - Prob. 40.24ECh. 40 - Prob. 40.25ECh. 40 - Prob. 40.26ECh. 40 - Prob. 40.27ECh. 40 - Prob. 40.28ECh. 40 - Prob. 40.29ECh. 40 - Prob. 40.30ECh. 40 - Prob. 40.31ECh. 40 - Prob. 40.32ECh. 40 - Prob. 40.33ECh. 40 - Prob. 40.34ECh. 40 - Prob. 40.35ECh. 40 - Prob. 40.36ECh. 40 - Prob. 40.37ECh. 40 - Prob. 40.38ECh. 40 - Prob. 40.39ECh. 40 - Prob. 40.40ECh. 40 - Prob. 40.41ECh. 40 - Prob. 40.42PCh. 40 - Prob. 40.43PCh. 40 - Prob. 40.44PCh. 40 - Prob. 40.45PCh. 40 - Prob. 40.46PCh. 40 - Prob. 40.47PCh. 40 - Prob. 40.48PCh. 40 - Prob. 40.49PCh. 40 - Prob. 40.50PCh. 40 - Prob. 40.51PCh. 40 - Prob. 40.52PCh. 40 - Prob. 40.53PCh. 40 - Prob. 40.54PCh. 40 - Prob. 40.55PCh. 40 - Prob. 40.56PCh. 40 - Prob. 40.57PCh. 40 - Prob. 40.58PCh. 40 - Prob. 40.59PCh. 40 - Prob. 40.60PCh. 40 - Prob. 40.61PCh. 40 - Prob. 40.62PCh. 40 - Prob. 40.63PCh. 40 - Prob. 40.64CPCh. 40 - Prob. 40.65CPCh. 40 - Prob. 40.66CPCh. 40 - Prob. 40.67PPCh. 40 - Prob. 40.68PPCh. 40 - Prob. 40.69PPCh. 40 - Prob. 40.70PP
Knowledge Booster
Similar questions
- 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_forwardAn electron is described by the wave function: ψ(x) = 0 for x < 0 ψ(x) = Ce^-x(1-e^-x) for x > 0, where x is in nanometres and C is a constant. (a) Find the value of C that normalizes ψ(x).(b) Where is the electron most likely to be found; that is, for what value of x is the probability of finding the electron largest?(c) Calculate < x > for this electron and compare your result with (b) above. Comment on the differences you find.arrow_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
- Let Ψ (x, t) = (A / (a2 + x2)) exp (-i 2 π E t / h ) be a normalized solution to Schrodinger’s equationfor constants A, a, and E.(a) What is A in terms of a?(b) What is the potential function V(x)?(c) Evaluate Δx Δp. Is the uncertainty principle satisfied?arrow_forwardImpurities in solids can be sometimes described by a particle-in-a-box model. Suppose He is substituted for Xe, and assume a particle-in-a-cubic-box model, the length of whose sides is equal to the atomic diameter of Xe (≈ 2.62 Å). Compute the lowest excitation energy for the He atom’s motion. (This is the energy difference between the ground state and the first excited state.)arrow_forwardBeing, Ψ = sin x, Φ = cos x and Θ = tan x, which of those functions could be a wave function?Why?arrow_forward
- 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.)arrow_forwardAn electron has a wavefunction ψ(x)=Ce-|x|/x0 where x0 is a constant and C=1/√x0 for normalization. For this case, obtain expressions for a. ⟨x⟩ and Δx in terms of x0. b. Also calculate the probability that the electron will be found within a standard deviation of its average position, that is, in the range ⟨x⟩-∆x to ⟨x⟩+∆x, and show that this is independent of x0.arrow_forwardAn electron in an infinitely deep square well has a wave function that is given by ψ3(x) = √2/Lsin (3πx/L)for 0 ≤ x ≤ L and is zero otherwise. (a) What are the most probable positions of the electron? (b) Explain how you identify them.arrow_forward
- 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 excited states. (b) How much energy must be supplied to excite the electron from the ground state to the sec- ond excited state? (c) From the second excited state, the electron drops down to the first excited state. How much energy is released in this process?arrow_forwardConsider the function f(z) = 2 sin (E (z - 4) + 4 State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding z-values. Enter the exact answers. Amplitude: A = Number Period: P = sin (a) Midline: y = Number The phase shift is let e L The vertical translation is cha te tae Hints for the maximum and minimum values of f (z): The maximum value of y = sin (I) is y= 1 and the corresponding z values are z = 공 and multiples of 2 x less than and more than this z value. You may want to solve (z - 4) = • The minimum value of y = sin (z) is y = -1 and the corresponding z values are z = 폭 and multiples of 2 less than and more than this z value. You may want to solve (z - 4) = . • If you get a value for z that is less than 0, you could add multiples of P to get into the next cycles. • If you get a value for z that is more than P, you could subtract multiples of P to get into…arrow_forwardThe planes of atoms in a particular cubic crystal lie parallel to the surface, 0.80 nm apart. X rays having wavelength 0.50 nm are directed at an angle θ to the surface. (a) For what values of θ will there be a strong refl ection? (b) What energy electrons could give the same result?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