Homework Help is Here – Start Your Trial Now!
Science
Chemistry
State the normalization condition for radial part of the atomic-orbital ?

State the normalization condition for radial part of the atomic-orbital ?

Chemistry by OpenStax (2015-05-04)
Chemistry by OpenStax (2015-05-04)
1st Edition
ISBN:9781938168390
Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Publisher:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Chapter16: Thermodynamics
Section: Chapter Questions
Problem 9E: Consider a system similar to the one in Figure 16.8, except that it contains six particles instead...
See similar textbooks
icon
Related questions
Question
100%

what is State the normalization condition for radial part of the atomic-orbital ?

this page will help in short answer please

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
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
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Atomic Structure and Spectra
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
  • SEE MORE QUESTIONS
Recommended textbooks for you
Chemistry by OpenStax (2015-05-04)
Chemistry by OpenStax (2015-05-04)
Chemistry
ISBN:
9781938168390
Author:
Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Publisher:
OpenStax
Introductory Chemistry For Today
Introductory Chemistry For Today
Chemistry
ISBN:
9781285644561
Author:
Seager
Publisher:
Cengage
General Chemistry - Standalone book (MindTap Cour…
General Chemistry - Standalone book (MindTap Cour…
Chemistry
ISBN:
9781305580343
Author:
Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:
Cengage Learning
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
World of Chemistry, 3rd edition
World of Chemistry, 3rd edition
Chemistry
ISBN:
9781133109655
Author:
Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Publisher:
Brooks / Cole / Cengage Learning
Physical Chemistry
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
SEE MORE TEXTBOOKS