P j grandinetti chem 4300 magnetism ang mom spin 56

Info icon This preview shows pages 56–62. Sign up to view the full content.

P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 56 / 62
Image of page 56

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Fine Structure of the H-Atom: All Together Executive Summary Adding in spin orbit and relativistic correction the total energy becomes E n , j = E ( 0 ) n + E ( 1 ) SO + E ( 1 ) r = E 1 n 2 [ 1 + ? 2 n 2 ( n j + 1 2 - 3 4 )] Our treatment of hydrogen atom fine structure stops here. We could go further with more energy refinements coming from couplings to nuclear degrees of freedom, and even couplings to the quantized electromagnetic field. P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 57 / 62
Image of page 57
Term Symbols P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 58 / 62
Image of page 58

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Term Symbols Atomic spectroscopists have devised approach for specifying set of states having particular set of 𝓁 , s , and j with a term symbol . Given 𝓁 , s , and j for electron term symbol is defined as 2 s + 1 { 𝓁 letter } j 2 s + 1 is called spin multiplicity 𝓁 letter is assigned based on numerical value of 𝓁 according to 𝓁 = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 numerical value { 𝓁 letter } S P D F G H I K L M O Q R T letter continuing afterwards in alphabetical order. Example What is term symbol for 2 states with j = 1 2 for p-electron? Solution: 𝓁 = 1 has symbol P, and spin multiplicity is 2 s + 1 = 2 1 2 + 1 = 2 . Thus we have 2 P 1 2 (pronounced “doublet P half.”) P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 59 / 62
Image of page 59
Term Symbols and Orbital Diagrams In orbital diagram e - is placed in box associated with 𝓁 and m 𝓁 with arrows indicating m s value. Possible orbital diagrams for 1s 1 which has 𝓁 = 0 , s = 1 2 , and j = 1 2 are Remember that we can add only one vector component of angular momentum vector in QM—conventionally it is the z component, so m j = m 𝓁 + m s . Both these orbital diagrams are associated with term symbol 2 S 1 2 (pronounced “doublet S half.”) P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 60 / 62
Image of page 60

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Example How are orbital diagrams for 2p 1 configuration associated with term symbols? Solution: Case of 2p 1 with 𝓁 = 1 and s = 1 2 can have j = 1 2 , 3 2 . This leads to possible terms of 2 P 1 2 and 2 P 3 2 , We can only associate 2 orbital diagrams with states j = 3 2 , m j = ± 3 2 . Other states are part of linear combinations belonging to 2 P 1 2 and 2 P 3 2 . More systematic approach uses Clebsch-Gordon series. P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 61 / 62
Image of page 61
Energy levels of the hydrogen atom. Taking both relativistic and spin-orbit energy corrections into account we arrive at energy level diagram of hydrogen labeled by “terms” P. J. Grandinetti (Chem. 4300) Magnetism, Ang. Mom., & Spin Nov 13, 2017 62 / 62
Image of page 62
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern