Recall: E=hν. A model that spans centuries. How do we understand the energetics and the structure of an atom? Sir Isaac Newton

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How do we understand the energetics and the structure of an atom? A model that spans centuries.

1860 Robert Bunsen (1811 1899) and Gustav Kirchhoff (1824 1887) discovered two alkali metals, cesium

The first fifty elements discovered beyond those known since ancient times were either the products

1 How do we understand the energetics and the structure of an atom? A model that spans centuries. Newton Bunson Rutherford Bohr Sir Isaac Newton Recall: E=hν Robert Bunsen ( ) Spectroscope In 1860 Robert Bunsen ( ) and Gustav Kirchhoff ( ) discovered two alkali metals, cesium (Cs) and rubidium (Rb). The first fifty elements discovered beyond those known since ancient times were either the products of chemical reactions or were released by electrolysis. From 1860 the search was on for trace elements detectable only with the help of specialized instruments like the spectroscope. 1

Hydrogen Line Spectrum Ernst Rutherford Balmer Series. 656.3nm 486.1nm 434.0nm Lyman Series. 121.6nm 102.6nm 97.3nm 95.

The first set, the Lyman series (n 1 = 1), occurs in the ultraviolet (UV) The second, the Balmer series (n 1 = 2), occurs

(1911) i) α-particles from a radioactive source were allowed to strike a thin gold foil.

Note: n 2 =(n 1 +1), R= 109678 cm -1 What did Rutherford expect?

2 Hydrogen Line Spectrum Ernst Rutherford Balmer Series nm 486.1nm 434.0nm Lyman Series nm 102.6nm 97.3nm 95.0nm Rydberg relationship A hydrogen spectrum consists of a repeating pattern of lines. The first set, the Lyman series (n 1 = 1), occurs in the ultraviolet (UV) The second, the Balmer series (n 1 = 2), occurs in the visible. The third, the Paschen series (n 1 = 3), occurs in the infrared (IR). Rutherford Scattering. (1911) i) α-particles from a radioactive source were allowed to strike a thin gold foil. ii) α-particles produce a tiny, visible flash of light upon hitting a fluorescent screen. Note: n 2 =(n 1 +1), R= cm -1 What did Rutherford expect? Thomsen had proposed a Raisin Bun Model For the Raisin Muffin Model More quantitatively At the turn of the century, the prevalent view of the atom was a positively charged blob with sprinkled negatively charged electron raisins in it. A uniform electric field would not deflect incoming alpha particles. 2

What did he observe? The dimensions of an atom. Rutherford's remark: "It was quite the most incredible event that ever happened to me in my life.

" α- particles were found at large deflection angles and some were back-scattered.

This was accomplished by determining the value of h. Louis de Broglie introduced the concept of matter waves In the shortest doctoral dissertation to date (3 pages).

3 What did he observe? The dimensions of an atom. Rutherford's remark: "It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you." α- particles were found at large deflection angles and some were back-scattered. The Shrödinger Equation Max Planck: in desperation, while attempting to remedy The ultra-violet catastrophe, introduced the concept of discrete energy levels. This was accomplished by determining the value of h. Louis de Broglie introduced the concept of matter waves In the shortest doctoral dissertation to date (3 pages). λ = h p Operators: Associated with each measurable parameter in a physical system is a quantum mechanical operator. Such operators arise because in quantum mechanics waves describe nature with (the wavefunction) rather than with discrete particles whose motion and dynamics can be described with the deterministic equations of Newtonian physics. 3

4 Requirements for a wavefunction The Shrödinger Equation and the H atom Orbital Size Orbital Shape Orbital Orientation The functions pass through a maximum at r = a o /Z This is the radial probability 4

Probability function of an s orbital 3-D The probability function is merely the square of the the wavefunction (Ψ).

This is also known as an electron density map or electron density.

zero probability at the nodes of the functions H-atom radial probabilities (1s,2s,3s) Radial probability of an s orbital.

5 Probability function of an s orbital 3-D The probability function is merely the square of the the wavefunction (Ψ). It is the probability of finding an electron at any point on a line drawn from the nucleus out to infinity. This is also known as an electron density map or electron density. The Born interpretation of wavefunction is that it represents The probability of finding an electron at some point (density) There is zero probability at the nodes of the functions H-atom radial probabilities (1s,2s,3s) Radial probability of an s orbital. 3-D The radial probability is the likelihood of finding an electron within successive spherical shells building out from the nucleus. Note that it has a value of 0 at the nucleus. Radial nodes occur in the frequency: s-orbitals (n-1) p-orbitals (n-2) d- orbitals (n-3) 5

6 H-atom radial Probabilities (2s, 2p) H-atom radial Probabilities (3s, 3p,3d) 2s has a high probability of being close to the nucleus- the 2p is only on average closer Orbital Planar Nodes. Summary Radial probability of a 3p orbital Nodal plane s p d # of planar nodes: s-orbitals = 0 p-orbitals = 1 d-orbitals = 2 Note the signs on the orbitals... These are important! Radial nodes. At a nodal plane (the nucleus) there is NO electron density and the sign of the orbital must change. 6

Penetration (why radial nodes are important) Qualitatively, the 3s orbital is lower in energy that the 3p orbitals and correspondingly the the 3 d orbitals.

BUT look more closely and notice the hump of probability very close to the nucleus, this lowers the energy of the 3s and 3p orbitals relative the the 3d and yields the observed trend.

Aufbau" means "to build-up". 1. e - are placed as close to the bottom of the energy level diagram as possible. 2.

7 Penetration (why radial nodes are important) Qualitatively, the 3s orbital is lower in energy that the 3p orbitals and correspondingly the the 3 d orbitals. Interestingly, from the probability profiles one might predict the opposite trend as the maximum probability of the 3s is furthest from the nucleus. BUT look more closely and notice the hump of probability very close to the nucleus, this lowers the energy of the 3s and 3p orbitals relative the the 3d and yields the observed trend.(less shielded) This also happens with the 2s and 2p orbitals. Aufbau Principle (variations in orbital energies) The Aufbau Principle is a series of procedures used when placing electrons on an atom. Aufbau" means "to build-up". 1. e - are placed as close to the bottom of the energy level diagram as possible. 2. The Pauli Exclusion Principle must be obeyed (an orbital will be limited to a maximum of two electrons). 3. Hund's Rule must be obeyed; when placing electrons into a degenerate set of orbitals, there must be one electron in each orbital of the set before any pairing of electrons can take place. Electronic Configurations Locations on the periodic table filling specific orbitals Cr and Cu are exceptions.why? The key lies in half and fully filled shells. See fig

Z eff = Z - σ Effective Nuclear Charge (Multi-electron atoms) The charge felt by an electron is NOT the nuclear charge Z. Slater s rules for Z eff If an electron resides in an s or p orbital: 1.

Electrons in the (n-1) shell contribute 0.85 to σ. 4. Electrons in deeper shells contribute 1.00 to σ. If the electron resides in a d or f orbital: 1. All inner-shell electrons (i.e., (n-1) and lower contribute uniformly 1 to σ.

8 Z eff = Z - σ Effective Nuclear Charge (Multi-electron atoms) The charge felt by an electron is NOT the nuclear charge Z. Slater s rules for Z eff If an electron resides in an s or p orbital: 1. All the electrons in in principle shells higher than the electron in question contributes 0 to σ. 2. Each electron in the same principle shell contributes 0.35 to σ. 3. Electrons in the (n-1) shell contribute 0.85 to σ. 4. Electrons in deeper shells contribute 1.00 to σ. If the electron resides in a d or f orbital: 1. All the electrons in in principle shells higher than the electron in question contributes 0 to σ. 2. Each electron in the same principle shell contributes 0.35 to σ. 3. All inner-shell electrons (i.e., (n-1) and lower contribute uniformly 1 to σ. The 2p orbital vanishes at the nucleus, therefore, the Penetration of the 2s electrons is greater at the core, and are LESS SHIELDED than the 2p electrons Z eff = Z - σ Effective Nuclear Charge (Example) Consider a 2p electron in a fluorine atom. Electron configuration: 1s 2 2s 2 2p 5 A Crude Summary of Slater s Rules Core electrons shield perfectly, valence electrons do not. Z eff increases in a period but remains relatively constant down a group. Electronic structure also impacts all other periodic trends. σ = (2x0.85)+(6x0.35) = = 3.8 Z eff = Z - σ = = 5.2 Note: the energy of an electron now depends upon n (the shell) and l the shape of the orbital. 8

Electronic configuration and periodic trends Ionization Potential 1. Different interpenetrations of AOs can be judged by the size of the orbitals, R(r) 2,

As a result of differing orbital penetrations and orientations electrons feel different effective nuclear charge. 4.

9 Electronic configuration and periodic trends Ionization Potential 1. Different interpenetrations of AOs can be judged by the size of the orbitals, R(r) 2, and the orientation of the orbitals. 2. As a result of different penetrations and orientations the Aufbau principle arises. 3. As a result of differing orbital penetrations and orientations electrons feel different effective nuclear charge. 4. Properties such as the first ionization energy follow and reflect electron configurations in a given group or period on the periodic table. Very stable! Ionization Potential Three hidden trends: 1. Maxima occur for noble gases - the result of stable closed shell configurations. 2. There is an increase from left to right in a period - arises from effective nuclear charge because of the additive effects of nuclear charge and imperfect shielding. 3. Steps in the increase in #2 - - shielding effects. For Li Ne period B C N: increases regularly but are lower than what would be extrapolated from Li Be this is the result of p electrons being less penetrating than s electrons. O F Ne :increases regularly but are lower than extrapolation from B C N. This is the result of filling the half full p-shell. The new electrons are repelled by columbic interactions Atomic Radii 3 types: 1. Single bond covalent: typical contribution to the length of a single bond. 2. VDW : obtained from NB approach between atoms. 3. Ionic radii : radii of atoms in ionic compounds. 2 trends: 1. Radii increase down the group. This arises from the successive use of orbitals in the same shells. 2. There is a decrease in radii across each period. This is in spite of more electrons being added. It underscores the influence of imperfect shielding. 9

Lecture January 18, Quantum Numbers Electronic Configurations Ionization Energies Effective Nuclear Charge Slater s Rules

Lecture January 18, Quantum Numbers Electronic Configurations Ionization Energies Effective Nuclear Charge Slater s Rules Lecture 3 362 January 18, 2019 Quantum Numbers Electronic Configurations Ionization Energies Effective Nuclear Charge Slater s Rules Inorganic Chemistry Chapter 1: Figure 1.4 Time independent Schrödinger