1

Views on Atomic Structure

Classical View – electrons and properties of electrons

Experiments with Light – Quantum Theory

Quantum View – behavior of electrons in atoms

2

Cathode Rays

Cathode rays are the carriers of electric current from cathode to anode inside a vacuumed tube

Cathode rays travel in straight lines

3

Cathode Rays

Cause glass and other materials to fluoresce

Deflect in a magnetic field similarly to negatively charged particles

4

J. J. Thomson’s Experiment

Devised an experiment to find the ratio of the cathode ray particle’s mass (me) to the charge (e)

me /e = –5.686 × 10–12 kg C–1

5

The Electron

coined the term “electron”

Millikan measured the charge on an electron - the famous “oil-drop” experiment

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Determined Electron Values

Robert Millikan then determined a value for the charge

e = –1.602 × 10–19 C

From m/e and the charge, the mass of an electron was determined to be

m = 9.109 × 10–31 kg/electron

7

J. J. Thomson – Atomic Model

Thomson proposed an atom with a positively charged sphere containing equally spaced electrons inside

RAISIN BUN MODEL

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Rutherford’s Model

Ernest Rutherford characterized alpha particles through an experiment and discovered the positive charge of an atom is concentrated in the center of an atom, the nucleus

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Rutherford’s Interpretation

10

Protons and Neutrons

From Rutherford’s experiments, he was able to determine the amount of positive nuclear charge

The positive charge was carried by particles called protons

Scientists introduced the atomic number, which represents the number of protons in the nucleus of an atom

James Chadwick discovered neutrons in the nucleus, which have nearly the same mass as protons and no charge

11

Mass Spectrometer

If a stream of positive ions having equal velocities is brought into a magnetic field, the lightest ions are deflected the most, making a tighter circle

12

Wave Motion

Caused by a displacement in a medium

Characterized by height of crest (or depth of trough)

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The Wave Nature of Light

Electromagnetic waves originate from the movement of electric chargesThe movement produces fluctuations in electric and magnetic fields

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Characterizing Waves

Electromagnetic radiation is characterized by its wavelength, frequency, and amplitude

Wavelength () is the distance between any two identical points in consecutive cycles

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Characterizing Waves

Frequency of a wave is the number of cycles of the wave that pass through a point in a unit of time

Amplitude of a wave is its height: the distance from a line of no disturbance through the center of the wave peak

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The Electromagnetic Spectrum

The electromagnetic spectrum is largely invisible to the eye

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The Electromagnetic Spectrum

• We can feel some radiation through other senses (infrared)

• Sunburned skin is a sign of too much ultraviolet radiation

• Materials vary in their ability to absorb or transmit different wavelengths– Our bodies absorb visible light, but transmit

most X rays– Window glass transmits visible light, but

absorbs ultraviolet radiation

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Continuous Spectra

White light passed through a prism produces a spectrum – colors in continuous form.

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The Continuous Spectrum

The different colors of light correspond to different wavelengths and frequencies

~ 650 nm ~ 575 nm

~ 500 nm

~ 480 nm

~ 450 nm

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Line Spectra

Light passed through a prism from an element produces a discontinuous spectrum of specific colors

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Line Spectra

The pattern of lines emitted by excited atoms of an element is unique

= atomic emission spectrum

22

Quantum Theory – Black Body Radiation

Planck proposed that the vibrating atoms in a heated solid could absorb or emit electromagnetic energy only in discrete amounts

Planck’s quantum hypothesis states that energy can be absorbed or emitted only as a quantum or as whole multiples of a quantum

The smallest amount of energy, a quantum, is given by:

E = hv

where h is Planck’s constant: = 6.626 × 10–34 J s

23

Quantum Theory – Photoelectric Effect

Einstein considered electromagnetic energy to be bundled into little packets called photons

Energy of photon is E = hv

Photoelectric Effect Movie

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Bohr’s Hydrogen Atom

Niels Bohr found that the electron energy (En) was quantized, that is, that it can have only certain specified values

Each specified energy value is called an energy level of the atom

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The Bohr Model

En = –B/n2 where B is a constant = 2.179 × 10–18 J and n is an integer

The negative sign represents the forces of attraction

The energy is zero when the electron is located infinitely far from the nucleus

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Bohr Explains Line Spectra

Bohr’s equation is most useful in determining the energy change (Elevel) that accompanies the leap of an electron from one energy level to anotherFor the final and initial levels:

f i2 2f i

B BE and E

n n

The energy difference between nf and ni is:

2 2 2 2f i i f

1 1B BE B

n n n n

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Energy Levels and Spectral Lines for Hydrogen

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Ground States and Excited States

Electrons in their lowest possible energy levels are in the ground state

Electrons promoted to any level n > 1 are in an excited state

Electrons are promoted by absorbing energye.g., electric discharge, heat, lasers (photons)

Electrons in an excited state eventually drop back down to the ground state “relaxation”

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Electronic TransitionsArrows represent transitions between energy levels

Upward arrows (a) show energy absorption, electrons move to higher energy levels

Downward arrows (b)–(d) represent energy release and relaxation

The length of an arrow is inversely proportional to photon wavelength

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Electronic Transitions

The length of an arrow is inversely proportional to photon wavelength

Shorter wavelengths, higher energies

Longer wavelengths, lower energies

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De Broglie’s Equation

•Louis de Broglie speculated that matter can behave as both particles and waves, just like light

•He proposed that a particle with a mass m moving at a speed v will have a wave nature consistent with a wavelength h

mv

32

Wave Functions ()

Quantum mechanics, or wave mechanics, is the treatment of atomic structure through the wavelike properties of the electron

Erwin Schrödinger developed an equation to describe the hydrogen atom

A wave function is a solution to the Schrödinger equation and represents an energy state of the atom

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Interpretation of a Wave Function

Wave mechanics provides a probability of where an electron will be in certain regions of an atom

The Born interpretation:The square of a wave function (2) gives the probability of finding an electron in a small

volume of space around the atom (orbital)

The interpretation leads to the idea of a cloud of electron density rather than a discrete location

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The Uncertainty Principle

Werner Heisenberg’s uncertainty principle states that we can’t simultaneously know exactly where a tiny particle like an electron is and exactly how it is moving

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The Uncertainty Principle

In light of the uncertainty principle, Bohr’s model of the hydrogen atom fails, in part, because it tells more than we can know with certainty

Electron is spread out like a wave; the wave which describes how the electron is distributed spacially is called a wave function)

36

Quantum Numbers and Atomic Orbitals

A wave function with a given set of these three quantum numbers is called an atomic orbital

In quantum mechanics the atomic orbitals require three integer quantum numbers to completely describe the energy and the shape of the 3-D space occupied by the electron (n, l, and ml)

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Principal Quantum Number (n)

• Is independent of the other two quantum numbers

• Can only be a positive integer

• indicates the size of an orbital (distance from the nucleus) and its electron energy

• n can be 1, 2, 3, 4, …

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Orbital Angular Momentum Quantum Number (l)

(aka Azimuthal quantum number)

• Determines the shape of the orbital: s, p, d, f which corresponds to values of l = 0, 1, 2, 3• Possible values: 0 to (n – 1); e.g., if n = 2, l can only be 0 or /1

• Each of these orbitals is a different region of space and a different shape

•All the ‘l’ quantum values represent different subshells

•When n = 1, there is only 1 “l” value meaning there is only one subshell in the first energy level; when n= 2; there are 2 values for ‘l’ indicating two subshells in the second energy level

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Magnetic Quantum Number (ml)

Determines the orientation in space of the orbital; so named because in a magnetic field, these different orientations have different energies

Possible values: –l to +l;e.g., if l = 2, ml can be –2, –1, 0, 1, 2

The magnetic quantum number defines the number of orbital in a shell. E.g. in the l = 0 subshell, there is only one ml value, therefore there is only orbital in this subshell; when l=1; there are 3 possible ml

values (-1, 0, +1) 3 orbitals in this subshell

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Taken together the three quantum numbers specific the orbital the electron occupies. Namely:the energy of the orbital, the shape of the orbital, and the orientation of the orbital .

Quantum Numbers Summary

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• writing 3 quantum numbers to indicate every possible orbital an electron can occupy is cumbersome; instead do we do the following:

• retain the numeric value of the principal quantum number and we use a letter to indicate the azimuthal quantum number:

• l = 0 s; l = 1 p; l = 2 d; l = 3 d• When combined, they indicate an a

specific orbital e.g. 1s orbital; 2s orbital; 2p orbital

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Radial Distributions

Electrons are most likely to reside nearest the nucleus because of electrostatic attraction

Probability of finding an electron decreases as distance (radius) from the nucleus increases

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Electron Probabilitiesand the 1s Orbital

The 1s orbital looks very much like a fuzzy ball, that is, the orbital has spherical symmetry (the probability of finding an electron is the same in direction)The electrons are more concentrated near the center

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Electron Probabilitiesand the 2s Orbital

The region near the nucleus is separated from the outer region by a spherical node - a spherical shell in which the electron probability is zero

EOS

The 2s orbital has two regions of high electron probability, both being spherical

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The Three p Orbitals-There are 3 p orbital; each orbital is cylindrically symmetrical with respect to rotation around one of the 3 axes, x, y, or z

Each ‘p’ orbital has two lobes of high probability density separated by a node (region of zero

probability)

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The Five d Orbitals

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Electron Spin (ms)

The electron spin quantum number explains some of the finer features of atomic emission spectra

Only possible values = –1/2 to +1/2

EOS

The spin refers to a magnetic field induced by the moving electric charge of the electron as it spins

48EOS

The Stern-Gerlach Experiment

Interaction of the electron spin with the magnetic field caused a splitting of the observed signal

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Summary of Concepts

• Cathode rays are negatively charged fundamental particles of matter, now called electrons

• An electron bears one fundamental unit of negative electric charge

• A nucleus of an atom consists of protons and neutrons and contains practically all the mass of an atom

• Mass spectrometry establishes atomic masses and relative abundances of the isotopes of an element

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Summary of Concepts

• Electromagnetic radiation is an energy transmission in the form of oscillating electric and magnetic fields

• The oscillations produce waves that are characterized by their frequencies (v), wavelengths (), and velocity (c)

• The complete span of possibilities for frequency and wavelength is described as the electromagnetic spectrum

51

Summary of Concepts

• Planck’s explanation of quantums gave us E = hv• The photoelectric effect is explained by thinking

of quanta of energy as concentrated into particles of light called photons

• Wave functions require the assignment of three quantum numbers: principal quantum number, n, orbital angular momentum quantum number, l, and magnetic quantum number, ml.

• Wave functions with acceptable values of the three quantum numbers are called atomic orbitals

52

Summary of Concepts

• Orbitals describe regions in an atom that have a high probability of containing an electron or a high electronic charge density

• Shapes associated with orbitals depend on the value of l. Thus, an s orbital (l = 0) is spherical and a p orbital (l = 1) is dumbbell-shaped

• A fourth quantum number is also required to characterize an electron in an orbital - the spin quantum number, ms