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

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 He 3d Li 3p Be 3s B e e e e C 2p Total Energy e e N 2s O Shell not full reactive Shell full stable e e 1s

Excellent question from last timeHund’s rule Why are each of the 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)

Screening in multi-electron atoms An atom of atomic number Z has a nucleus of charge +Ze and Z electrons of charge –e each. Electrons in outer shells “see” a nucleus of charge +Zeffe, where Zeff < Z, because the nuclear charge is partially “screened” by electrons in the inner shells. This equation works when one electron is screened from the nucleus by other electrons. Warning: Eqn 41.43 is wrong except for hydrogen. Screening is important.

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 ?

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)

Effect of 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 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

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

Goals for Chapter 42 To understand the bonds holding atoms together To see how rotation and vibration of molecules affect spectra To learn how and why atoms form crystalline structures To apply the energy-band concept to solids To develop a model for the physical properties of metals To learn how impurities affect semiconductors and to see applications for semiconductors To learn about superconductivity

Four types of molecular bonds Ionic bonds: Binding between two oppositely charged ionized atoms (e.g. Na+ and Cl-) Covalent bonds: Egalitarian participation of electron clouds Van der Waals bonds: (interaction between electric dipole moments of atoms and molecules E~0.1 eV e.g. water molecules, H2, O2 and N2) Hydrogen bonds: a proton, i.e. H+ ion, gets between two atoms and polarizes them creating induced dipole moments (e.g. polyethylene)

Ionic bonds Electron clouds of ions tend to overlap An ionic bond is an interaction between oppositely charged ionized atoms. Figure on the right shows a graph of the potential energy of two oppositely charged ions. NaCl is a typical example. (Na+ and Cl-) Another example: Mg2+ and (Cl-)2 with two ions.

Covalent bonds In a covalent bond, the wave functions are distorted and become more concentrated in certain places. Figure on the right shows the hydrogen covalent bond, and Figure below shows the methane molecule. Need opposite signs by the Pauli principle

Clicker question on molecular bonds The difference between an ionic bond and a covalent bond is A. ionic bonds are only found in crystals such as sodium chloride (NaCl) where there are many atoms in close proximity. B. covalent bonds are only found in molecules with three or more atoms. C. ionic bonds are highly directional, while covalent bonds are not. D. ionic bonds involve the transfer of an electron from one atom to another, while covalent bonds involve electrons that spend much of their time between atoms. Answer: D

A42.1 The difference between an ionic bond and a covalent bond is A. ionic bonds are only found in crystals such as sodium chloride (NaCl) where there are many atoms in close proximity. B. covalent bonds are only found in molecules with three or more atoms. C. ionic bonds are highly directional, while covalent bonds are not. D. ionic bonds involve the transfer of an electron from one atom to another, while covalent bonds involve electrons that spend much of their time between atoms.

Rotational energy levels for diatomic molecules Figure shows a model of a diatomic molecule. PHYS 170, rotational motion where I is the moment of inertia and ω is the angular velocity. Now quantize

Rotational energy levels for diatomic molecules Figure shows a model of a diatomic molecule. For a diatomic molecule composed of two point-like elements, separated by distance r0 with masses m1 and m2

Rotational energy levels for diatomic molecules Figure (right) shows some rotational energy levels for a diatomic molecule.

Vibrational energy levels of a diatomic molecule Figure on the left shows a model of a diatomic molecule.

Vibrational energy levels of diatomic molecules Figure on the right shows some vibrational energy levels of a diatomic molecule. Quantize a two-mass harmonic oscillator to find the energy levels (mr is again the reduced mass).

Rotation and vibrational levels combined Figure 42.8 (right) shows an energy-level diagram for rotational and vibrational energy levels of a diatomic molecule. Figure 42.9 (below) shows a typical molecular band spectrum.