PHY274: Atomic Structure V Wolfgang Pauli Implications of Pauli Exclusion Principle Shells, Periodic Table of Elements X-ray Spectroscopy
Announcements Wednesday November 8, Review for Midterm II Try out the practice test, which is posted on the course website. Friday November 10, University celebrates Veteran’s Day (one day early !). No class. Midterm II, Monday November 13 Bring notecard and calculator. Wednesday Nov 15, Start Chapter 42 (Molecules and Solid State).
Implications of QM for chemistry Electron configuration in atoms: How do the electrons fit into the available orbitals? What are energies of orbitals? 3d 3p 3s 2p Total Energy 2s 1s 3
Review: Implications of QM for chemistry Electron configuration in atoms: How do the electrons fit into the available orbitals? What are energies of orbitals? Filling orbitals … lowest to highest energy, 2 e’s per orbital H Oxygen = 1s2 2s2 2p4 3d He 3p Li 3s Be B e e e e 2p Total Energy e e C 2s N Shell not full reactive Shell full stable O e e 1s 4
Schrodinger predicts wave functions and energies l=0 l=1 l=2 4p 3d 4s m=-2,-1,0,1,2 Li 3p Energy 3s Na 2p 2s m=-1,0,1 Why would the behavior of Li be similar to Na? because shape of outermost electron is similar. because energy of outermost electron is similar. c. both a and b d. some other reason 1s 5
Schrodinger predicts wave functions and energies l=0 l=1 l=2 4p 3d 4s m=-2,-1,0,1,2 Li 3p Energy 3s Na 2p 2s m=-1,0,1 Why would the behavior of Li be similar to Na? because shape of outermost electron is similar. because energy of outermost electron is similar. c. both a and b d. some other reason 1s ✔ 6
B. An n=3 to n=2 hydrogen transition Q.41.1 The 21cm hydrogen line (energy 5.87 μeV) is the result of which of the following transitions: A. Spin-Orbit (electron spin – orbital angular momentum) coupling with l changing by one unit. B. An n=3 to n=2 hydrogen transition C. A “spin-flip” transition (due to electron spin-nuclear spin interaction) in hydrogen. D. An ml=1 to ml=0 hydrogen transition C
B. An n=3 to n=2 hydrogen transition Q.41.1 The 21cm hydrogen line (energy 5.87 μeV) is the result of the following transition: A. Spin-Orbit (electron spin – orbital angular momentum) coupling with l changing by one unit. B. An n=3 to n=2 hydrogen transition C. A “spin-flip” transition (due to electron spin-nuclear spin interaction) D. An ml=1 to ml=0 hydrogen transition C
In helium, which of the following statements is true ? Q.41.2 In helium, which of the following statements is true ? A. There is one electron in the 1s state and one in the 2s state. The valence electron in the 2s state allows helium to be reactive. B. There are two electrons in the 1s state with opposite szvalues to satisfy the Pauli exclusion principle. Since there are no extra valence electrons, helium is a “noble” gas. C. Helium has two electrons in the 2s state with oppositely oriented spins. Hence, helium is non-reactive. D. Helium and Lithium have identical QM electronic structures. B
In helium, which of the following statements is true ? Q.41.2 In helium, which of the following statements is true ? A. There is one electron in the 1s state and one in the 2s state. The valence electron in the 2s state allows helium to be reactive. B. There are two electrons in the 1s state with opposite szvalues to satisfy the Pauli exclusion principle. Since there are no extra valence electrons, helium is a “noble” gas. C. Helium has two electrons in the 2s state with oppositely oriented spins. Hence, helium is non-reactive. D. Helium and Lithium have identical QM electronic structures. B
Q.41.3 2,1,0 B
Q.41.3 2,1,0 B
Q.41.4 First fill up the 1S, then 2S and then 2p levels2,2,5 A
First fill up the 1s, then 2s and then 2p levels2,2,5 A Q.41.4 First fill up the 1s, then 2s and then 2p levels2,2,5 A First fill up the 1S, then 2S and then 2p levels2,2,5 A
Ground-state electron configurations 15
Ground-state electron configurations (Zoom in) Question: What is special about the elements with arrows ? 16
The Periodic Table and Quantum Mechanics 17
The periodic table and Quantum Mechanics 18
Interesting question Hund’s rule Why are each of the higher ml orbitals filled with one electron before putting two electrons into an orbital ? Ans: This is “Hund’s rule” in physical chemistry. Yes, but why does Hund’s rule work ? Lower energy first (magnetic force is weaker)
The Periodic Table and Quantum Mechanics The outer electrons (“valence electrons”) determine the chemical properties of elements e.g. Na 1s22s22p63s (outer electron loosely bound valence +1); Cl 1s22s22p63s23p5 (missing one electron valence -1) Individually dangerous elements but you can eat NaCl. e.g. He, Ne, Ar are noble gases; all electron states are filled. Real bumper sticker sold by the American Chemical Society. 20
X-ray spectroscopy When atoms are bombarded with high-energy electrons, x rays are emitted. There is a continuous spectrum of x rays (“bremsstrahlung”) as well as strong characteristic x-ray emission at certain definite wavelengths (see the peaks labeled Kα and Kβ on the right). Question: What does the German word “bremsstrahlung” mean ? Ans: braking radiation “braking” = “deceleration”
X-ray spectroscopy: Moseley’s law Moseley showed that the square root of the x-ray frequency in Kα emission is proportional to Z – 1, where Z is the atomic number of the atom (see the Figure below). Larger Z means a higher frequency and more energetic emitted x-ray photons. This is consistent with our model of multielectron atoms. Bombarding an atom with a high-energy electron can knock an atomic electron out of the innermost K shell. Kα x rays are produced when an electron from the L shell falls into the K-shell vacancy. The energy of an electron in each shell depends on Z, so the x-ray energy released does as well. Killed at age 27 in WWI (slaughter in Gallipoli)
PHYS272: Gauss’ Law Electric field is determined by the charge enclosed in the Gaussian sphere 23
A multielectron atom and “screening” The figure on the right is a sketch of a lithium atom, which has 3 electrons. The allowed electron states are naturally arranged in shells of different size centered on the nucleus. The n = 1 states make up the K shell, the n = 2 states make up the L shell, and so on. Due to the Pauli exclusion principle, the 1s subshell of the K shell (n = 1, l = 0, ml = 0) can accommodate only two electrons (one with ms = + 1/2, one with ms = –1/2). Hence the third electron goes into the 2s subshell of the L shell (n = 2, l = 0, ml = 0). 24
Effect of Screening. Energy levels of multi-electrons with screening Example: Suppose an electron in the L shell (n=2) drops down to the K shell (n=1) and emits an x-ray photon. What is the energy of the photon ? Use E=hf to obtain Mosley’s Law
X-ray spectroscopy: Example for gun-shot residue X-ray emission spectrum Atoms of different elements emit characteristic x rays at different frequencies and wavelengths. Hence the characteristic x-ray spectrum of a sample can be used to determine the atomic composition of the sample. Lead, Antimony, Barium
An astrophysics example: a supernova remmant
Also find absorption lines in the x-ray band
Clicker question on screening Ordinary hydrogen has one electron and one proton. It requires 10.2 eV of energy to take an electron from the innermost (K) shell in hydrogen and move it into the next (L) shell. Uranium has 92 electrons and 92 protons. The energy required to move an electron from the K shell to the L shell of uranium is A. (91)(10.2 eV). B. (92)(10.2 eV). C. (91)2(10.2 eV). D. (92)2(10.2 eV). E. none of the above Answer: C
Clicker question on screening Ordinary hydrogen has one electron and one proton. It requires 10.2 eV of energy to take an electron from the innermost (K) shell in hydrogen and move it into the next (L) shell. Uranium has 92 electrons and 92 protons. The energy required to move an electron from the K shell to the L shell of uranium is A. (91)(10.2 eV). B. (92)(10.2 eV). C. (91)2(10.2 eV). D. (92)2(10.2 eV). E. none of the above Answer: C
What element is this ? What is its electron configuration ? 4p 3d 4s What is the electron configuration for an atom with 20 electrons ? (Write it out !) 3p 3s Energy a. 1s2, 2s2, 2p6, 3s2, 3p4 b. 1s2, 2s2, 2p6, 3s2, 3p6, 3d2 2p c. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d6 2s d. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2 e. none of the above 1s 31
What element is this ? What is its electron configuration ? 4p 3d 4s What is the electron configuration for an atom with 20 electrons ? (Write it out !) 3p 3s Energy a. 1s2, 2s2, 2p6, 3s2, 3p4 b. 1s2, 2s2, 2p6, 3s2, 3p6, 3d2 2p c. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d6 2s d. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2 e. none of the above Answer is d! Calcium: Fills lowest energy levels first. Which orbitals are occupied determines chemical behavior (bonding, reactivity, “alkaline earth”) 1s 32
For next week Moving on to QM of Molecules and Solid State. Read material in advance Concepts require wrestling with material