mse 3300-lecture note 02-chapter 02 atomic structure

Chapter 2 - MSE 3300 / 5300 UTA Spring 2015

Lecture 2. Atomic Structure & Interatomic Bonding (1)

Learning Objectives After this lecture, you should be able to do the following:

1. Name the two atomic models cited and note the differences between them 2. Describe the important quantum-mechanical principle that relates to electron energies. 3. Understand the four electron quantum numbers that characterize electrons in an atom.

Reading • Chapter 2: Atomic Structure (2.1–2.4)

Multimedia • Atomic structure overview: https://www.youtube.com/watch?v=pV822HfqT44 • Atoms, orbitals and periodic table: https://www.youtube.com/watch?v=ZpJFJd0Zg-c

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Virtual Materials Science & Engineering (VMSE)

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• This is a screenshot of the VMSE opening window (Wiley)

• Available at http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/

Chapter 1 - MSE 3300 / 5300 UTA Fall 2014

Review: Lecture 1. Introduction Learning Objectives After this lecture, you should be able to do the following:

1. What is Materials Science and Engineering? 2. List six different property classifications of materials 3. Cite the four components that are involved in the design, production, and utilization of materials. Describe the interrelationships between these components. 4. List the three primary classifications of solid materials

Reading • Chapter 1: Introduction

Multimedia • What Is Materials Science? https://www.youtube.com/watch?v=bobe-r8VCho 3

Chapter 1 - MSE 3300 / 5300 UTA Fall 2014

What is Materials Science and Engineering?

• What is Materials Science and Materials Engineering?

• Structure? Subatomic, atomic, microscopic, and macroscopic

• Property? Mechanical, electrical, thermal, magnetic, optical, deteriorative (External stimuli – Response)

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Materials Science

Materials Engineering Materials Engineering Four Components


Atomic Structure

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Atomic Structure

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Carbon 12 (12C) (A = 12.00000)

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Chapter 2 - MSE 3300 / 5300 UTA Spring 2015 8

Atomic Structure (Freshman Chem.) • atom – electrons – 9.11 x 10-31 kg

protons neutrons

• atomic number (Z) = # of protons in nucleus of atom = # of electrons in neutral species

• A [=] atomic mass unit = amu = 1/12 mass of 12C Atomic weight = wt of 6.022 x 1023 molecules or atoms 1 amu/atom = 1 g/mol

C 12.011 H 1.008 etc.

} 1.67 x 10-27 kg


Atomic Structure (Freshman Chem.) • Atomic mass (A)

• Isotope: Atoms of some elements that have two or more different atomic masses

* Although the number of protons is the same for all atoms of a given element, the number of neutrons (N) may be variable.

• Mole: In one mole of a substance, there are 6.022 X 1023 atoms or molecules.

1 amu/atom (or molecule) = 1 g/mol Ex. Atomic weight of iron: 55.85 amu/atom or 55.85 g/mol


Electrons in Atoms: Bohr atomic model

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Quantum Mechanics: Wave-Mechanical Model

• A wave function (Ψ) is a mathematical function that relates the location of an electron at a given point in space (identified by x, y, and z coordinates) to the amplitude of its wave, which corresponds to its energy. Thus each wave function is associated with a particular energy E.

• The square of the wave function at a given point (Ψ2) is proportional to the probability of finding an electron at that point (probability density).

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Hydrogen Atom: Binding Energies (En)

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Wave Functions (Orbitals)

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Probability Density Plots of S-Orbitals

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Radial Probability Distributions (RPD) for S-Orbitals

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17

X



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* The peak corresponds to the most probable radius for the electron, 52.9 pm, which is exactly the radius predicted by Bohr’s model of the hydrogen atom.



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(a) Electron probability. Note the presence of circular regions, or nodes, where the probability density is zero.

(b) Contour surfaces enclose 90% of the electron probability, which illustrates the different sizes of the 1s, 2s, and 3s orbitals. The orange color corresponds to regions of space where the phase of the wave function is positive, and the blue color corresponds to regions of space where the phase of the wave function is negative.

(c) Electron probability as a function of distance from the nucleus (r). The most probable radius (rmp) increases as n increases, but the 2s and 3s orbitals have regions of significant electron probability at small values of r.


P Orbitals

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• Unlike s orbitals, p orbitals have θ and φ dependence. P orbitals _____________ spherically symmetrical.

• p orbitals consist of two lobes (of opposite sign) separated by a _____________ plane on which Ψ = 0 (and Ψ2 = 0).

• There is zero probability of finding a p-electron in a nodal plane. Thus, there is ________ probability of finding a p-electron at the nucleus.


Electron Orbitals

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Radial Probability Distributions (RPD)

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Fourth Quantum Number: Electron Spin • From quantum mechanics, a fourth quantum number appears that describes

the spin of an electron within an orbital (an intrinsic property of electron). • Spin magnetic quantum number, ______ • There is no classical analogy to spin. An electron can have two spin states: ms

= ________ (spin up) or ms = _______ (spin down).

• ms completes the description of an electron and is NOT dependent on the orbital.

So we can describe a given orbital using three quantum numbers (n, l, ml) and a given electron using 4 quantum numbers (n, l, ml, ms).

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Pauli Exclusion Principle • No two electrons in the same atom can have the same four quantum numbers.

In other words, no two electrons can be in the same orbital and have the same spin.

• The Pauli exclusion principle limits an atom to ________ electrons per orbital.

• How many electrons in a single atom can have the following two quantum numbers: n = 4 and ml

= -2? _______

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Electron Distribution: Bohr and Wave-Mechanical Atom Models

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Bohr and Wave-Mechanical Atom Models

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Electronic Structure • Electrons have wavelike and particulate properties. • Two of the wavelike characteristics are

– electrons are in orbitals defined by a probability. – each orbital at discrete energy level is determined by

quantum numbers.

– Quantum # Designation n = principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.) = subsidiary (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1) ml = magnetic 1, 3, 5, 7 (- to +) ms = spin ½, -½


Summary: Quantum Numbers and Numbers of Orbitals and Electrons

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Electron Energy States

1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4

• have discrete energy states • tend to occupy lowest available energy state.

Electrons...

Adapted from Fig. 2.6, Callister & Rethwisch 9e. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, p. 22. Copyright © 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)


Relative Energies of the Electrons for the Shells and Subshells

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Example: Filled and Lowest Unfilled Energy States for a Sodium Atom

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• Why? Valence (outer) shell usually not filled completely.

• Most elements: Electron configuration not stable. SURVEY OF ELEMENTS

Electron configuration

(stable)

...

... 1s 2 2s 2 2p 6 3s 2 3p 6 (stable) ... 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic #

18 ... 36

Element 1s 1 1 Hydrogen 1s 2 2 Helium 1s 2 2s 1 3 Lithium 1s 2 2s 2 4 Beryllium 1s 2 2s 2 2p 1 5 Boron 1s 2 2s 2 2p 2 6 Carbon

... 1s 2 2s 2 2p 6 (stable) 10 Neon 1s 2 2s 2 2p 6 3s 1 11 Sodium 1s 2 2s 2 2p 6 3s 2 12 Magnesium 1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

... Argon ... Krypton

Adapted from Table 2.2, Callister & Rethwisch 9e.


Electron Configurations • Valence electrons – those in unfilled shells • Filled shells more stable • Valence electrons are most available for

bonding and tend to control the chemical properties – example: C (atomic number = 6)

1s2 2s2 2p2

valence electrons


Electronic Configurations ex: Fe - atomic # = 26

valence electrons

1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4

1s2 2s2 2p6 3s2 3p6 3d 6 4s2

Adapted from Fig. 2.6, Callister & Rethwisch 9e. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, p. 22. Copyright © 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)


The Periodic Table • Columns: Similar Valence Structure

Adapted from Fig. 2.8, Callister & Rethwisch 9e.

Electropositive elements: Readily give up electrons to become + ions.

Electronegative elements: Readily acquire electrons to become - ions.

give

up

1e-

give

up

2e-

give

up

3e-

iner

t gas

es

acce

pt 1

e-

acce

pt 2

e-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y


• Ranges from 0.9 to 4.1,

Smaller electronegativity Larger electronegativity

• Large values: tendency to acquire electrons.

Electronegativity


Atomic Structure

• Some of the following properties 1) Chemical 2) Electrical 3) Thermal 4) Optical

are determined by electronic structure


Summary 1. Two atomic models

2. Quantum-mechanical principle that relates to electron energies Interrelationships between these components.

3. Four electron quantum numbers that characterize electrons in an atom

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Electron Spin and Magnetism

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mse 3300-lecture note 02-chapter 02 atomic structure

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