Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 36, Problem 47P
(a)
To determine
The energy of the eight electron in harmonic oscillator potential and in its lowest-energy state.
(b)
To determine
The lowest energy of the eight spin-1 particles in harmonic oscillator potential
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(4) Electronic energy level of a hydrogen atom is given by
R
E
; n =
n2
1, 2, 3,...
and R = 13.6 eV. Each energy level has degeneracy 2n² (degeneracy is the number of equivalent
configurations associated with the energy level).
(a) Calculate the partition function Z for a hydrogen atom at a constant temperature.
(b) Let us consider that the energy level of a hydrogen atom is approximated by a two level
system, n = 1,2. Estimate the mean energy at 300 K.
Comparisons of the energy differences between two states with that predicted by theory can test the theoretical model. For the case of the muon g-value, there's a small discrepancy between it and the Standard Model of particle physics. We can see atomic transitions in cesium in atomic clocks. We can measure the frequency by applying pulses at frequencies to observe the resonance (see the provided equation, Rabi's formula).
Consider a spin-1/2 particle that precesses in a magnetic field in the z direction. The probability of the particle being spin up or spin down along z doesn’t vary with time. The states |+z> and |—z> are stationary states of the Hamiltonian H-hat = ω0 S-hatz. If we alter the Hamiltonian by applying in addition an oscillating magnetic field transverse to the z axis, we can induce transitions between these two states by properly adjusting the frequency of this transverse field. The energy difference E+—E_ = h-bar ω0 can then be measured with high accuracy. This…
(a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is ac/n, where a is
the fine structure constant, equal to e/4neghc. (b) What would be the speed in a hydrogen
like atom with a nuclear charge of Ze?
Chapter 36 Solutions
Essential University Physics
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 11ECh. 36 - Prob. 12ECh. 36 - Prob. 13ECh. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34ECh. 36 - Prob. 35ECh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Solar physicists measure the strong magnetic...Ch. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
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
- What is the probability that an electron in the base state of the hydrogen atom will be found inside the nucleus? (let the radius of the nucleus be r).arrow_forwardAssume that the nucleus of an atom can be regarded as a three-dimensional box of width 2:10-¹4 m. If a proton moves as a particle in this box, find (a) the ground-state energy of proton in MeV and (b) the energies of the first excited state. (c) What are the degenerates of these states? Constants: h = 6.626-10-34 [J-s], m = 1.673-10-27 [kg] and ħ=h/2π.arrow_forward(4) Electronic energy level of a hydrogen atom is given by R ; п %3D 1,2, 3,... n2 E = - and R = 13.6 eV. Each energy level has degeneracy 2n2 (degeneracy is the number of equivalent configurations associated with the energy level). (a) Derive the partition function for a hydrogen atom at a constant temperature. (b) Consider that the energy level of a hydrogen atom is approximated by a two level system, n = 1,2. Estimate the mean energy at 300 K.arrow_forward
- A spin half particle is prepared in the spin state |S) = 2|+) + (1 + V3i)l-). where |S) = |S - n = th). What is the component în of spin of the particle which is known to be th?arrow_forwardAssume that there is an isotropic hyperfine interaction between electron and nucleus (or nuclei). Using first order perturbation theory to calculate the energies of all possible spin states. Also calculate the possible ESR transitions between these states. Draw the energy level diagram and ESR spectrum. Assume you have positive isotropic coupling constant. You have electron with S=1/2 and one nucleus with I=2arrow_forwardIn atoms there is a finite, though very small, probability that, at some instant, an orbital electron will actually be found inside the nucleus. In fact, some unstable nuclei use this occasional appearance of the electron to decay by electron capture. Assuming that the proton itself is a sphere of radius 1.1 * 10-15 m and that the wave function of the hydrogen atom’s electron holds all the way to the proton’s center, use the ground-state wave function to calculate the probability that the hydrogen atom’s electron is inside its nucleus.arrow_forward
- (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.arrow_forwarda) What is the magnitude of angular momentum of 3d-2 orbital of H-atom. b) Given that the spin functions, a(@) and B(@), are eigenfunctions of s' and S, operators. Find the eigenvalues of S' and S, when applied to a (@) and B(@) spin functions.arrow_forwardFind the binding energy of the hydrogen electron for states with the following principal quantum numbers. (Note the binding energy is just the absolute value of the Energy level, the energy required to remove the electron from that state to infinity.) a) For n = 3. b) For n = 5. c) For n = 7.arrow_forward
- What is the maximum kinetic energy of an electron such that a collision between the electron and a stationary hydrogen atom in its ground state is definitely elastic?arrow_forwardFor a 3d electron in an external magnetic field of 2.50 × 10-3 T, find (a) the current associated with the orbital angular momentum, and (b) the maximum torque.arrow_forwardCheck Your Understanding Can the magnitude of Lzever be equal to L?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
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning