Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 5.18P
To determine
The ground state energy of positronium.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In terms of the totally antisymmetric E-symbol (Levi-Civita tensor) with €123 = +1, the vector product
can be written as
(A x B) i = tijk Aj Bk,
where i, j, k = 1, 2, 3 and summation over repeated indices (here j and k) is implied.
i)
ii)
iii)
iv)
For general vectors A and B, using (2) prove the following relations:
a) A x B=-B x A
b) (A x B) A = (A x B) - B = 0.
The Levi-Civita symbol is related to the Kronecker delta. Prove the following very useful
formula
€ijk€ilm = 8j18km - Sjm³ki.
(2)
Prove the formula
(3)
€imn€jmn = 2dij.
Assuming that (3) is true (and using antisymmetry of the E-symbol), prove the relation
A x (B x C) = (AC) B- (AB) C
An electron is confined in the ground state of a one-dimensional har-
monic oscillator such that V((r – (x))²) = 10-10 m. Find the energy (in
eV) required to excite it to its first excited state.
(Hint: The virial theorem can help.]
Evaluate the lifetime (in seconds) of the transition |2, 1,0) → |1,0,0) of hydrogen.
Chapter 5 Solutions
Modern Physics For Scientists And Engineers
Ch. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.26PCh. 5 - Prob. 5.27P
Knowledge Booster
Similar questions
- (3.8) This question introduces a rather efficient method for calculating the mean and variance of probability distributions. We define the moment generating function M(t) for a random variable x by M(t) = (etx). Show that this definition implies that (x) = M(n) (0), (3.51) (3.52) where M(n) (t) mean (x) = d" M/dt" and further that the M (¹) (0) and the variance σ = = M(2)(0) [M(¹) (0)] 2. Hence show that: - (a) for a single Bernoulli trial, = M(t) pe 1-p; (3.53) (b) for the binomial distribution, M(t) = (pe +1 - p)"; (3.54) (c) for the Poisson distribution, M(t) = em(et-1); (3.55) (d) for the exponential distribution, λ M(t) (3.56) Hence derive the mean and variance in each case and show that they agree with the results derived earlier.arrow_forwardpost |Consider a system which is in the state, Y(0,4) =Y,"(0,ø)+ J¿r,"(0,ø)+Y'(0,$), where Y," (0,4) are the spherical harmonics. If Î, is measured what possible values can be obtained? (a) –ħ,0,ħ (b) +ħ‚2ħ,-ħ (c) +ħ,3ħ,-ħ (d) +ħ,-ħ (е) 3h, 2harrow_forwardConsider a proton confined within typical nuclear dimensions of 5×10^(−15) m. Estimate the minimum kinetic energy of the proton. Repeat this calculation for an electron confined within typical nuclear dimensions. Comment briefly on the physical significance of your results, given that the nuclear binding energy for a proton is typically in the range 1−10 MeVarrow_forward
- Calculate the following quantities for a three-dimensional classical ideal gas: (a) (vx), (b) (v?). (c) (v*vx), (d) (vàvy), (e) ((Vx + () (v²v?). bv,)^) (b a constant),arrow_forwardProblem 4.25 If electron, radius [4.138] 4πεmc2 What would be the velocity of a point on the "equator" in m /s if it were a classical solid sphere with a given angular momentum of (1/2) h? (The classical electron radius, re, is obtained by assuming that the mass of the electron can be attributed to the energy stored in its electric field with the help of Einstein's formula E = mc2). Does this model make sense? (In fact, the experimentally determined radius of the electron is much smaller than re, making this problem worse).arrow_forwardDerive Eq.(7.13) by using set of equations (7.2 a,b,c and d).arrow_forward
- A neutron of mass m of energy E a,V(x) = +V ) II. Estimate the kinetic energy of the nucleons when they reach region II.arrow_forwardIn quantum statistical mechanics, generalize Eq. (4.10) to the case of a mixture of several different species of non-interacting particles.arrow_forwardThe process of beta decay of the atomic nucleus can be visualized as perturbation of the effect (_e^2/r). Calculate the first correction on the electron energy for the case represented by the following function •SU(06/0=(2/2) + (2)arrow_forward
- 1.10 The OPERA experiment was designed to search for v, → Vv, appearance. A beam of muon neutrinos with average energy 17 GeV travels 732 km from CERN to the detector in the LNGS laboratory. Assuming a simple model for oscillations between two flavour states with a mixing angle 6 Am? = 2 x 10-3eV?, calculate the probability for a neutrino to be seen as a v, at the OPERA detector. 45° and a mass difference squared of %3D The OPERA detector is made of emulsion films interleaved with lead plates. What property of lead makes it a good choice for this type of detector?arrow_forward(b) Calculate the half width in nanometers for Doppler broadening of the 4s S 4p transition for atomic nickel at 361.939 nm (3619.39 Å) at a temperature of 20,000 K in both wavelength and frequency units. (e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculatedin (e). (g) Create a spreadsheet to calculate the Doppler half width DlD in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K. (h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that they describe. Explain in detail how two of these sources originate in sample atoms.arrow_forwardWhat are the values of the following integrals relevant to the description of a hydrogen- like atom. In each case provide the work that justifies your answer. (If an answer is written without work or explanation it won't be counted). (a) ( W43,–1,} | V4,4,–1,- ). (b) (v,3,–1,} | Ħ |W43,-1. ). (c) (¼43,-1, | J: |44,3,-1, )- | J: | W43,–1,} )- 4,3,–1, (d) ( V4,3,–1,} | Sz |W4,-3,1 -3,-1. ).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON