week 1 introduction

Prepared by:Mrs Faraziehan Senusi

PA-A11-7C

Quantum Theory

Atomic Orbitals

Electronic Configuration

Chapter 1Atoms, Molecules & Chemical bonding

Molecular Orbitals

Bonding and Intermolecular Compounds

David P. White Prentice Hall ©

2003

Introduction

The Discovery of Atomic Structure

The Modern View of Atomic Structure

The Wave Nature of Light

Quantized Energy and Photons

Line Spectra and the Bohr Model

The Dual Nature of Electron

Introduction


• The ancient Greeks were the first to postulate that matter consists of indivisible constituents.

• Later scientists realized that the atom consisted of charged entities.


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Humphry Davy (1778–1829)

Michael Faraday (1791–1867)

George Stoney (1826–1911)

J. J. Thomson (1856–1940)

Robert Millikan (1868–1953)

Ernest Rutherford (1871–1937


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Cathode Rays and Electrons

• A cathode ray tube (CRT) is a hollow vessel with an electrode at either end.

• A high voltage is applied across the electrodes.• The voltage causes negative particles to move from

the negative electrode to the positive electrode.• The path of the electrons can be altered by the

presence of a magnetic field.



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• Consider cathode rays leaving the positive electrode through a small hole.– If they interact with a magnetic field perpendicular to

an applied electric field, the cathode rays can be deflected by different amounts.

– The amount of deflection of the cathode rays depends on the applied magnetic and electric fields.

– In turn, the amount of deflection also depends on the charge to mass ratio of the electron.

• In 1897, Thomson determined the charge to mass ratio of an electron to be 1.76 108 C/g.


C~coulomb


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Consider the following experiment:• Oil drops are sprayed above a positively charged plate

containing a small hole. • As the oil drops fall through the hole, they are given a

negative charge.• Gravity forces the drops downward. The applied electric

field forces the drops upward.• When a drop is perfectly balanced, the weight of the drop

is equal to the electrostatic force of attraction between the drop and the positive plate.



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• Using this experiment, Millikan determined the charge on the electron to be 1.60 10-19 C.

• Knowing the charge to mass ratio, 1.76 108 C/g, Millikan calculated the mass of the electron: 9.10 10-28 g.

• With more accurate numbers, we get the mass of the electron to be 9.10939 10-28 g.



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RadioactivityConsider the following experiment:• A radioactive substance is placed in a shield

containing a small hole so that a beam of radiation is emitted from the hole.

• The radiation is passed between two electrically charged plates and detected.

• Three spots are noted on the detector:– a spot in the direction of the positive plate, – a spot which is not affected by the electric field,– a spot in the direction of the negative plate.



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• A high deflection towards the positive plate corresponds to radiation which is negatively charged and of low mass. This is called b-radiation (consists of electrons).

• No deflection corresponds to neutral radiation. This is called g-radiation.

• Small deflection towards the negatively charged plate corresponds to high mass, positively charged radiation. This is called a-radiation.


• From the separation of radiation we conclude that the atom consists of neutral, positively, and negatively charged entities.

• Thomson assumed all these charged species were found in a sphere.


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The Nuclear Atom• Rutherford carried out the following experiment:• A source of a-particles was placed at the mouth of a

circular detector.• The a -particles were shot through a piece of gold

foil.• Most of the a-particles went straight through the foil

without deflection.• Some a-particles were deflected at high angles.• If the Thomson model of the atom was correct, then

Rutherford’s result was impossible.



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• In order to get the majority of -particles through a piece of foil to be undeflected, the majority of the atom must consist of a low mass, diffuse negative charge - the electron.

• To account for the small number of high deflections of the -particles, the center or nucleus of the atom must consist of a dense positive charge.


• Rutherford modified Thomson’s model as follows:– assume the atom is spherical

but the positive charge must be located at the center, with a diffuse negative charge surrounding it


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• The atom consists of positive, negative, and neutral entities (protons, electrons, and neutrons).

• Protons and neutrons are located in the nucleus of the atom, which is small. Most of the mass of the atom is due to the nucleus.– There can be a variable number of neutrons for

the same number of protons. Isotopes have the same number of protons but different numbers of neutrons.

• Electrons are located outside of the nucleus. Most of the volume of the atom is due to electrons.


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The structure of the atom• Matter consists of very small, indivisible particles,

which are named atoms• Atoms are made up of subatomic particles - p, n & e

– Electron: negative charge, – Theories about the energy and the arrangement of

electrons in atoms are based on the interaction of matter with electromagnetic radiation.

• Dual nature of electron : wave & particle


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Summary

• Atoms are made up of protons, neutrons and electrons.• The charges of protons, neutrons and electrons and their

relative masses are as shown below:


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Particle Symbol Relative electric charge

ProtonNeutronElectron

pnE

+10-1


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• All types of electromagnetic radiation, or radiant energy, can be described in the terminology of waves.

• All waves have a characteristic length, height & number of waves that pass through a certain point in one second

wavelength, l amplitude, A frequency, n

• The frequency of electromagnetic radiation is related to its wavelength by:


cc = speed of electromagnetic waves/ speed of light


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• Electromagnetic radiation moves through a vacuum with a speed of 2.99792458 108m/s. ~ 3.00 108 m/s

• Electromagnetic waves have characteristic wavelengths and frequencies.

• The electromagnetic radiation most obvious to us is visible light. Visible light represents only a tiny segment of the electromagnetic radiation spectrum.

• Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).



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• Under certain conditions, it is also possible to describe light as composed of particles, or photons.

• According Max Planck (1858–1947), each photon

of light has a particular amount (a quantum) of energy.

• The amount of energy possessed by a photon depends on the frequency of the light.


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• Planck: energy can only be absorbed or released from atoms in certain small amounts called a quantum (=Fixed quantity of energy).

• The relationship between energy and frequency is

where h is Planck’s constant (6.626 10-34 J.s).• There is an important relationship between energy

and wavelength of radiation:

hE

hc

E



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• Einstein assumed that light traveled in energy packets (stream of particles) called photons.

• According to Einstein, each photon can transfer its energy to a single electron during a collision.

• The energy of one photon:

hE


• Number of electrons ejected proportional to intensityMore intense more photonsThus more electrons ejected


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Photoelectric Effect

• In 1913, Niels Bohr (1885–1962) described the electron of a hydrogen atom as revolving around its nucleus in circular orbits.

• Each orbit has a particular energy and it associated with electron motion must be fixed value or quantized.

• It suggest that electrons can only be in certain discrete orbits, and that they absorb or emit energy in discrete amounts as they move from one orbit to another.

• Each orbit thus corresponds to a definite energy level for the electron.


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• Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.

• After lots of math, Bohr showed that

where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else).

218 1

J 1018.2n

E



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• The first orbit in the Bohr model has n = 1, is closest to the nucleus, and has negative energy by convention.

• The furthest orbit in the Bohr model has n close to infinity and corresponds to zero energy.

• The amount energy needed to move an electron in the Bohr atom depend on the difference in energy levels between the initial and final states.



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• The differences between the energies of the initial and final states is given by

• We can show that

• When ni > nf ,energy is emitted.

• When nf > ni , energy is absorbed

2218 11

J 1018.2if nn

hchE


hEEE if

Bohr Model

The energy levels in the hydrogen atom and the various emission series.

Each energy level corresponds to the energy associated with an allowed energy state for an orbit.



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• Light waves can behave like a stream of particles (photons), then perhaps particles such as electrons can possess wave properties.

• Using Einstein’s and Planck’s equations, de Broglie showed the particle and wave properties are related by:

• The momentum, mv, is a particle property, whereas is a wave property.

• de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

The Dual Nature of the Electron

mvh

• In 1927, the German physicist Werner Heisenberg postulated the uncertainty principle, which states that it is impossible to know the exact position and momentum (mass times speed) of a particle simultaneously.

• Heisenberg’s Uncertainty Principle:

It is impossible to determine accurately both the momentum and the position of an electron (or any other very small particle) simultaneously.


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The Heisenberg’s Uncertainty Principle


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• The principle is expressed mathematically as

where Δx is the uncertainty in position and Δmv is the uncertainty in momentum.

• The uncertainty principle has profound implications for an atomic model. It means that we cannot assign fixed paths for electrons, such as the circular orbits of Bohr's model.

4·

hmvx


• Acceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the field of quantum mechanics, which examines the wave nature of objects on the atomic scale.

• In 1926, Erwin Schrodinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom.


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week 1 introduction

Technology

david white

positive plate

high mass

negative particles

positive electrode

negative plate

mass ratio

small deflection