
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
thumb_up100%
what is State the normalization condition for radial part of the atomic-orbital ?
this page will help in short answer please

Transcribed Image Text:TABLE 6.4
The first few associated Laguerre polynomials.
n = 1,
n = 2,
n = 3,
n = 4,
1=0
1=0
1 = 1
1=0
1 = 1
1=2
1=0
1 = 1
1 = 2
1=3
L(x) = -1
L₂(x) = -2!(2-x)
L3(x) = -3!
L₁(x) = -3!(3 - 3x + 1x²)
L(x)=-4!(4x)
L(x) = -5!
L₁(x) = −4!(4 - 6x + 2x² − £x³)
L3(x) = -5!(10-5x + x²)
L(x) = -6!(6-x)
L'(x) = -7!
The functions given by Equation 6.47 may look complicated, but notice that each
one is just a polynomial multiplied by an exponential. The combinatorial factor in front
assures that the R₁ (r) are normalized with respect to an integration over r, or that the
R₁(r) satisfy
R² (r) R (r) r²dr = 1
Note that the volume element here is rdr, which is the "r" part of the spherical
coordinate volume element r² sin @drdodo.
The complete hydrogen atomic wave functions are
(6.48)
(6.49)
nim (r, 0, 0) = R₁ (r) Y™ (0, 0)
The first few hydrogen atomic wave functions are given in Table 6.5. The normalization
condition for hydrogen atomic wave functions is
[drr² de sino dom (r, 0, 0)nim (r, 0, 0) = 1
Because Ĥ is Hermitian (Section 4-5), the functions must also be orthogonal.
This orthogonality relationship is given by
(6.50)
f" drr² ["* de sine f
S™ dom (r, 0, 0)nim (r, 0, 0) = Enn Summ (6.51)
where the 8's are Krönecker deltas (Equation 4.30).
207
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 1 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Similar questions
- Question 36 of 43 Submit Write the complete ground-state electron configuration of F. 1 2 3 4) 5 6 pdf 1 4 5 6. 9. 10arrow_forwardGive correct detailed Solution with explanation needed...don't give Handwritten answer...don't copy answer anywhere..don't use Ai for answering thisarrow_forwardWhen an electron goes into an orbit in the Bohr model (Select all that apply) O energy is given off there is an attractive interaction energy is absorbed there is a repulsive interaction O The energy of the atom will be higher.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill EducationPrinciples of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning
- Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill EducationChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningElementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY

Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning

Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education

Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning

Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education

Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning

Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY