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A great and very useful lecture on Modern Physics. These lecture slides include: Atomic Physics, Atomic Structure and the Periodic Table, Pauli Exclusion Principle, Atomic Structure, Lanthanides, Actinides, Angular Momentum, Lscoupling, Anomalous Zeeman Effect
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What distinguished Mendeleev was not only genius, but a passion for the elements. They became his personal friends; he knew every quirk and detail of their behavior.
What would happen if there are more than one electron? a nucleus with charge +2e attracting two electrons. the two electrons repelling one another. Can not solve problems exactly with the Schrödinger equation because of the complex potential interactions. Can understand experimental results without computing the wave functions of many-electron atoms by applying the boundary conditions and selection rules.
Hydrogen : ( n , ℓ, m ℓ, ms ) = (1, 0, 0, ±½) in ground state. In the absence of a magnetic field, the state ms = ½ is degenerate with the ms = −½ state. Helium : (1, 0, 0, ½) for the first electron. (1, 0, 0, −½) for the second electron. Electrons have antialigned ( ms = +½ and ms = −½) spins as being paired. Supports Pauli exclusion principle. The principle quantum number also has letter codes. n = 1 2 3 4... Letter = K L M N… n = shells (eg: K shell, L shell, etc.) n ℓ = subshells (eg: 1 s , 2 p , 3 d ) Electrons for H and He atoms are in the K shell. H: 1 s^2 He: 1 s^1 or 1 s
How many electrons may be in each subshell? Recall: ℓ = 0 1 2 3 4 5 … letter = s p d f g h … ℓ = 0, ( s state) can have two electrons. ℓ = 1, ( p state) can have six electrons, and so on. The lower ℓ values have more elliptical orbits than the higher ℓ values. Electrons with higher ℓ values are more shielded from the nuclear charge. Electrons lie higher in energy than those with lower ℓ values. 4 s fills before 3 d. Total For each m ℓ: two values of ms 2 For each ℓ: (2ℓ + 1) values of m ℓ 2(2ℓ + 1)
Groups : Vertical columns. Same number of electrons in an ℓ orbit. Can form similar chemical bonds. Periods : Horizontal rows. Correspond to filling of the subshells. Some properties of elements are compared by the ionization energies of elements and atomic radii.
Inert Gases : Last group of the periodic table Closed p subshell except helium Zero net spin and large ionization energy Their atoms interact weakly with each other Alkalis : Single s electron outside an inner core Easily form positive ions with a charge +1e Lowest ionization energies Electrical conductivity is relatively good Alkaline Earths : Two s electrons in outer subshell Largest atomic radii High electrical conductivity
Lanthanides ( rare earths ) : Have the outside 6 s 2 subshell completed As occurs in the 3 d subshell, the electrons in the 4 f subshell have unpaired electrons that align themselves The large orbital angular momentum contributes to the large ferromagnetic effects Actinides : Inner subshells are being filled while the 7 s 2 subshell is complete Difficult to obtain chemical data because they are all radioactive Have longer half-lives
L , Lz , S , SzJ and Jz are quantized. Orbital angular momentum Spin angular momentum Total angular momentum
An effect of the spins of the electron and the orbital angular momentum interaction is called spin-orbit coupling. is the magnetic field due to the proton.
No external magnetic field : Only Jz can be known because the uncertainty principle forbids Jx or J y from being known at the same time as J z
Now the selection rules for a single-electron atom become Δ n = anything Δℓ = ± 1 Δ mj = 0, ± 1 Δ j = 0, ± 1 Hydrogen energy-level diagram for n = 2 and n = 3 with the spin- orbit splitting.
Hund’s rules :
The notation for a single-electron atom becomes n^2 S +1^ LJ The letters and numbers are called spectroscopic symbols. There are singlet states ( S = 0) and triplet states ( S = 1) for two electrons.
There are separated energy levels according to whether they are S = 0 or 1. Allowed transitions must have Δ S = 0. No allowed ( forbidden ) transitions are possible between singlet and triplet states with much lower probability.
