University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
14th Edition
ISBN: 9780321982582
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 41, Problem 41.21DQ
(a)
To determine
To show: The orbital
(b)
To determine
Whether the result in part (a) is applicable to classical object.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(a) Find the mass density of a proton, modeling it as a solid sphere of radius 1.00 x 10-15 m. (b) What If? Consider a classical model of an electron as a uniform solid sphere with the same density as the proton. Find its radius. (c) Imagine that this electron possesses spin angular momentum Iω = h/2 because of classical rotation about the z axis. Determine the speed of a point on the equator of the electron. (d) State how this speed compares with the speed of light.
(a) Calculate: (i) the energy spacing AE between the ground state and the first excited
state of the hydrogen atom; (ii) and the ratio AE/E between the spacing and the ground state
energy.
(b) Consider now a macroscopic system: a simple pendulum which consists of a 5 g mass
attached to a 2 m long, massless and inextensible string. Calculate (i) the total energy E1 of
the pendulum when the string makes an angle of 60° with the vertical; (ii) the frequeney of the
pendulum's small oscillations and the energy AE of one quantum; and (iii) the ratio AE/E1.
(c) Examine the sizes of the ratio AE/E1 calculated in parts (a) and (b) and comment on
the importance of the quantum effects for the hydrogen atom and the pendulum.
(a) Predict the energy in eV of a photon emitted in a transition from the first excited state to the ground state in eV for a system consisting of a nucleus containing Z = 50 protons and just one electron. You need not recapitulate the entire derivation for the Bohr model, but think carefully about the changes you have to make to take into account the factor Z.
(b) The negative muon (μ−) behaves like a heavy electron, with the same charge as the electron but with a mass 207 times as large as the electron mass. As a moving μ− comes to rest in matter, it tends to knock electrons out of atoms and settle down onto a nucleus to form a "one-muon" atom. For a system consisting of a nucleus of platinum (Pt195 with 78 protons and 117 neutrons) and just one negative muon, predict the energy in eV of a photon emitted in a transition from the first excited state to the ground state. The high-energy photons emitted by transitions between energy levels in such "muonic atoms" are easily observed in…
Chapter 41 Solutions
University Physics with Modern Physics Plus Mastering Physics with eText -- Access Card Package (14th Edition)
Ch. 41.1 - Prob. 41.1TYUCh. 41.2 - Prob. 41.2TYUCh. 41.3 - Prob. 41.3TYUCh. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYUCh. 41.7 - Prob. 41.7TYUCh. 41.8 - Prob. 41.8TYUCh. 41 - Prob. 41.1DQCh. 41 - Prob. 41.2DQ
Ch. 41 - Prob. 41.3DQCh. 41 - Prob. 41.4DQCh. 41 - Prob. 41.5DQCh. 41 - Prob. 41.6DQCh. 41 - Prob. 41.7DQCh. 41 - In the ground state of the helium atom one...Ch. 41 - Prob. 41.9DQCh. 41 - Prob. 41.10DQCh. 41 - Prob. 41.11DQCh. 41 - Prob. 41.12DQCh. 41 - Prob. 41.13DQCh. 41 - Prob. 41.14DQCh. 41 - Prob. 41.15DQCh. 41 - Prob. 41.16DQCh. 41 - Prob. 41.17DQCh. 41 - Prob. 41.18DQCh. 41 - Prob. 41.19DQCh. 41 - Prob. 41.20DQCh. 41 - Prob. 41.21DQCh. 41 - Prob. 41.22DQCh. 41 - Prob. 41.23DQCh. 41 - Prob. 41.1ECh. 41 - Prob. 41.2ECh. 41 - Prob. 41.3ECh. 41 - Prob. 41.4ECh. 41 - Prob. 41.5ECh. 41 - Prob. 41.6ECh. 41 - Prob. 41.7ECh. 41 - Prob. 41.8ECh. 41 - Prob. 41.9ECh. 41 - Prob. 41.10ECh. 41 - Prob. 41.11ECh. 41 - Prob. 41.12ECh. 41 - Prob. 41.13ECh. 41 - Prob. 41.14ECh. 41 - Prob. 41.15ECh. 41 - Prob. 41.16ECh. 41 - Prob. 41.17ECh. 41 - Prob. 41.18ECh. 41 - A hydrogen atom in a 3p state is placed in a...Ch. 41 - Prob. 41.20ECh. 41 - Prob. 41.21ECh. 41 - Prob. 41.22ECh. 41 - Prob. 41.23ECh. 41 - Prob. 41.24ECh. 41 - Prob. 41.25ECh. 41 - Prob. 41.26ECh. 41 - Prob. 41.27ECh. 41 - Prob. 41.28ECh. 41 - Prob. 41.29ECh. 41 - (a) Write out the ground-state electron...Ch. 41 - Prob. 41.31ECh. 41 - Prob. 41.32ECh. 41 - Prob. 41.33ECh. 41 - Prob. 41.34ECh. 41 - Prob. 41.35ECh. 41 - Prob. 41.36ECh. 41 - Prob. 41.37ECh. 41 - Prob. 41.38ECh. 41 - Prob. 41.39PCh. 41 - Prob. 41.40PCh. 41 - Prob. 41.41PCh. 41 - Prob. 41.42PCh. 41 - Prob. 41.43PCh. 41 - Prob. 41.44PCh. 41 - Prob. 41.45PCh. 41 - Prob. 41.46PCh. 41 - Prob. 41.47PCh. 41 - Prob. 41.48PCh. 41 - Prob. 41.49PCh. 41 - Prob. 41.50PCh. 41 - Prob. 41.51PCh. 41 - Prob. 41.52PCh. 41 - Prob. 41.53PCh. 41 - Prob. 41.54PCh. 41 - Prob. 41.55PCh. 41 - Prob. 41.56PCh. 41 - Prob. 41.57PCh. 41 - Effective Magnetic Field. An electron in a...Ch. 41 - Prob. 41.59PCh. 41 - Prob. 41.60PCh. 41 - Prob. 41.61PCh. 41 - Prob. 41.62PCh. 41 - Prob. 41.63PCh. 41 - Prob. 41.64PCh. 41 - Prob. 41.65PCh. 41 - Prob. 41.66PCh. 41 - Prob. 41.67PCh. 41 - Prob. 41.68CPCh. 41 - Prob. 41.69CPCh. 41 - Prob. 41.70PPCh. 41 - Prob. 41.71PPCh. 41 - Prob. 41.72PPCh. 41 - Prob. 41.73PP
Knowledge Booster
Similar questions
- Suppose an clectron is in a state described by the wave function 1 (e“ sin 6 + cos 0) g(r), V4 where | 19(r) |² r² dr = 1, and o, 0 are the azimuth and polar angles respectively. (a) What are the possible results of a measurement of the z-component Lz of the angular momentun of the electron in this state? (b) What is the probability of obtaining each of the possible results in part (a)? (c) What is the expectation value of L¿?arrow_forward(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state? in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in Karrow_forward(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state?in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in Karrow_forward
- a) How many distinct angles from the vertical axis can the orbital angular momentum vector L make for an electron with l = 7? b)Calculate the smallest possible angle the L can make with respect to the vertical axis. (Hint: The smallest angle occurs when ml takes the maximum allowed value. Sketch L in that case and compare the vertical component, which is related to ml, to the magnitude of L, which is related to l.)arrow_forwardThis question is for modern physics and wave and particle: (a) To how small a region must an electron be confined for borderline relativistic speeds – say, 0.05c – to become reasonably likely? (Ans: 3.9×10^−12m ) (b) On the basis of this, would you expect relativistic effects to be prominent for hydrogen’s electron, which has an orbit radius near 10-10? For a lead atom “inner-shell” electron of orbit radius 10-12m?arrow_forwardIn a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å: (a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton.arrow_forward
- Angular momentum is best expressed as a vector, 1= (!,!y,lz). In quantum mechanics, the corresponding operators are given by: L = (Îz, Îy, Îz), where, Î, = -ih (y dz Îy Î, = -ih (r- -ih 2. dz (a) Evaluate | L4, Ly and express your result in terms of L̟. (Hint: In this case, your placeholder function should be f(x, y, z).)arrow_forwardIn a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å:(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton. (b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)? (c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 Å separation?arrow_forward2. The angular part of the wavefunction for an electron bound in a hydrogen atom is: Y(0,0) = C(5Y²³ +Y? +Yº° ), where Y₁™ (0,0) are normalized spherical harmonics. (a) What is the value of normalization constant C?arrow_forward
- (a) A quantum dot can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third lowest energy level, E3, to the lowest energy level, E₁, in such a well. Take the sides of the cubic box to be of length L = 3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³¹ kg. for each of the E₁ and E3 energy (b) Specify the degree of degeneracy levels, explaining your reasoning.arrow_forwardYou have the energy matrix for only 4x4 elements. Calculate the expected value of energy (E) using the function 1 1 -fox /2 e -3icut 2 [e heo S 0 0 0 2 E= = 5 0 0 e 0 2 0 0 0 Ther 2 J Al Laxities (E) A8l 2 gidd) dasll Cuaal l o |2 l Jiew /2 Vi *[fi“ e 0:‘ 5arrow_forwardConsider a two-electron atom in which the electrons, orbiting a nucleus of charge+Ze, follow Bohr-like orbits of the same radius r, with the electrons always on opposite sides of the nucleus. (a) Show that the net force on each electron is toward the nucleus and has magnitude. (b) Use the fact that this is the centripetal force to show that the square of each electron’s orbital speed v is given by as attached.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning