Download One Electron Atomic - Advanced Quantum Chemistry and Spectroscopy - Lecture Slides and more Slides Chemistry in PDF only on Docsity! Spin related to spin and orbital magnetic moments, µs and µL of the H-atom: e L e s zLLzss LLss m e m e LS LS Zz 2 −=−= == == γγ γµγµ γµγµ rrrr rrrr γ = “magnetogyric ratio” of the electron (having mass me) is a positive quantity since the charge on the electron is negative. e B m e 2 h =µ has units of a magnetic dipole and is called a Bohr magneton. The quantity µB = 9.274 x 10-24 J T-1 in SI units docsity.com 4.3: One electron atomic (Zeeman) spectroscopy For a single electron problem (H-atom, Na atom, etc) we expect the following: µx µy µx µy µz ψ2,1,-1ψ2,1,1ψ2,1,0ψ2,0,0 ψn,l,ml = ψ1,0,0 1s 2s 2p Expect: 1 line (2s, 2p orbitals are degenerate) but see 3 lines. µ here is the dipole moment operator: More on this later. docsity.com The Anomalous Zeeman Effect (not anomalous at all!) In a very high magnetic field, the Zeeman triplet is found to be further split. This is known as the anomalous Zeeman effect. no field magnetic field high magnetic field To explain this Goudsmit and Uhlenbeck in 1925 proposed that the electron has an intrinsic (built-in) magnetic moment independent of the orbital angular momentum. This intrinsic angular momentum results in a magnetic dipole moment that also interacts with an external magnetic field, resulting in the high field splitting. The concept of electron spin was introduced. The spin of a particle is its intrinsic angular momentum (not due to its angular motion). The spin is a fixed characteristic of a particle, like its charge. To a guarded extent, we can make an classical analogy that the electron is a sphere of charge spinning which results in an intrinsic angular momentum. This analogy is the origin of its name. However, spin is a purely quantum mechanical phenomenon without a true classical analogue. docsity.com Experimental verification of electron spin: Stern-Gerlach experiment z B ∂ ∂ = docsity.com Nobel Prize on a post card! Gerlach's postcard, dated 8 February 1922, to Niels Bohr. It shows a photograph of the beam splitting, with the message, in translation: "Attached [is] the experimental proof of directional quantization. We congratulate [you] on the confirmation of your theory." docsity.com Consider H-atom with smmn ,,, ll ψ ( ) ( ) s ss mmnsB mmns B mmnmz mm mm ,,, ,,,,,, 2 2ˆ l ll ll lll hh h ψµ ψµψµ +−= +−=Then: Hence the force in the z-direction Fz is given by: ( ) z BmmF sBz ∂ ∂ +−= 2l r µ Consider 1s and 2s orbitals: z B z BF msmn BBz s ∂ ∂ = ∂ ∂ ±−=∴ ±===== µµ m r l l 2 12 2 1 2 1001 docsity.com ms=1/2 ms=1/2 ms=-1/2 ms=-1/2 2s 1s docsity.com 12 == lnConsider 2p orbitals z Bc z Bb z Ba deflectionmmn B B B s ∂ ∂ +±− ∂ ∂ −± ∂ ∂ ± µ µ µ 2,0 2 1112) 0,2 2 1112) 2 1012) m l l docsity.com
