Loading...

PPT – Quantum Mechanics of Atoms PowerPoint presentation | free to view - id: 12c886-ZjZiM

The Adobe Flash plugin is needed to view this content

Chapter 28 Quantum Mechanics of Atoms

Units of Chapter 28

- Quantum Mechanics A New Theory
- The Wave Function and Its Interpretation the

Double-Slit Experiment - The Heisenberg Uncertainty Principle
- Philosophic Implications Probability versus

Determinism - Quantum-Mechanical View of Atoms
- Quantum Mechanics of the Hydrogen Atom Quantum

Numbers

Units of Chapter 28

- Complex Atoms the Exclusion Principle
- The Periodic Table of Elements
- X-Ray Spectra and Atomic Number
- Fluorescence and Phosphorescence
- Lasers
- Holography

28.1 Quantum Mechanics A New Theory

Quantum mechanics incorporates wave-particle

duality, and successfully explains energy states

in complex atoms and molecules, the relative

brightness of spectral lines, and many other

phenomena. It is widely accepted as being the

fundamental theory underlying all physical

processes.

28.1 Quantum Mechanics A New Theory

Quantum mechanics is essential to understanding

atoms and molecules, but can also have effects on

larger scales.

28.2 The Wave Function and Its Interpretation

the Double-Slit Experiment

An electromagnetic wave has oscillating electric

and magnetic fields. What is oscillating in a

matter wave?

28.2 The Wave Function and Its Interpretation

the Double-Slit Experiment

This role is played by the wave function, ?. The

square of the wave function at any point is

proportional to the number of electrons expected

to be found there. For a single electron, the

wave function is the probability of finding the

electron at that point.

28.2 The Wave Function and Its Interpretation

the Double-Slit Experiment

For example the interference pattern is observed

after many electrons have gone through the slits.

If we send the electrons through one at a time,

we cannot predict the path any

single electron will take, but we can predict the

overall distribution.

28.3 The Heisenberg Uncertainty Principle

Quantum mechanics tells us there are limits to

measurement not because of the limits of our

instruments, but inherently.

28.3 The Heisenberg Uncertainty Principle

This is due to the wave-particle duality, and to

interaction between the observing equipment and

the object being observed.

28.3 The Heisenberg Uncertainty Principle

Imagine trying to see an electron with a powerful

microscope. At least one photon must scatter off

the electron and enter the microscope, but in

doing so it will transfer some of its momentum to

the electron.

28.3 The Heisenberg Uncertainty Principle

The uncertainty in the momentum of the electron

is taken to be the momentum of the photon it

could transfer anywhere from none to all of its

momentum. In addition, the position can only be

measured to about one wavelength of the photon.

28.3 The Heisenberg Uncertainty Principle

Combining, we find the combination of

uncertainties

This is called the Heisenberg uncertainty

principle. It tells us that the position and

momentum cannot simultaneously be measured with

precision.

28.3 The Heisenberg Uncertainty Principle

This relation can also be written as a relation

between the uncertainty in time and the

uncertainty in energy

This says that if an energy state only lasts for

a limited time, its energy will be uncertain. It

also says that conservation of energy can be

violated if the time is short enough.

28.4 Philosophic Implications Probability versus

Determinism

The world of Newtonian mechanics is a

deterministic one. If you know the forces on an

object and its initial velocity, you can predict

where it will go.

28.4 Philosophic Implications Probability versus

Determinism

Quantum mechanics is very different you can

predict what masses of electrons will do, but

have no idea what any individual one will.

28.5 Quantum-Mechanical View of Atoms

Since we cannot say exactly where an electron is,

the Bohr picture of the atom, with electrons in

neat orbits, cannot be correct.

Quantum theory describes an electron probability

distribution this figure shows the distribution

for the ground state of hydrogen

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

- There are four different quantum numbers needed

to specify the state of an electron in an atom. - Principal quantum number n gives the total

energy

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

2. Orbital quantum number l gives the angular

momentum l can take on integer values from 0 to

n - 1.

(28-3)

3. The magnetic quantum number, ml, gives the

direction of the electrons angular momentum, and

can take on integer values from l to l.

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

This plot indicates the quantization of angular

momentum direction for l 2. The other two

components of the angular momentum are undefined.

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

4. The spin quantum number, ms, which for an

electron can take on the values ½ and -½. The

need for this quantum number was found by

experiment spin is an intrinsically quantum

mechanical quantity, although it mathematically

behaves as a form of angular momentum.

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

This table summarizes the four quantum numbers.

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

The angular momentum quantum numbers do not

affect the energy level much, but they do change

the spatial distribution of the electron cloud.

28.6 Quantum Mechanics of the Hydrogen Atom

Quantum Numbers

Allowed transitions between energy levels occur

between states whose value of l differ by one

Other, forbidden, transitions also occur but

with much lower probability.

28.7 Complex Atoms the Exclusion Principle

Complex atoms contain more than one electron, so

the interaction between electrons must be

accounted for in the energy levels. This means

that the energy depends on both n and l. A

neutral atom has Z electrons, as well as Z

protons in its nucleus. Z is called the atomic

number.

28.7 Complex Atoms the Exclusion Principle

In order to understand the electron distributions

in atoms, another principle is needed. This is

the Pauli exclusion principle No two electrons

in an atom can occupy the same quantum state. The

quantum state is specified by the four quantum

numbers no two electrons can have the same set.

28.7 Complex Atoms the Exclusion Principle

This chart shows the occupied and some

unoccupied states in He, Li, and Na.

28.8 The Periodic Table of the Elements

We can now understand the organization of the

periodic table. Electrons with the same n are in

the same shell. Electrons with the same n and l

are in the same subshell. The exclusion

principle limits the maximum number of electrons

in each subshell to 2(2l 1).

28.8 The Periodic Table of the Elements

Each value of l is given its own letter symbol.

28.8 The Periodic Table of the Elements

Electron configurations are written by giving the

value for n, the letter code for l, and the

number of electrons in the subshell as a

superscript. For example, here is the

ground-state configuration of sodium

28.8 The Periodic Table of the Elements

This table shows the configuration of the outer

electrons only.

28.8 The Periodic Table of the Elements

Atoms with the same number of electrons in their

outer shells have similar chemical behavior. They

appear in the same column of the periodic table.

28.8 The Periodic Table of the Elements

The outer columns those with full, almost full,

or almost empty outer shells are the most

distinctive. The inner columns, with partly

filled shells, have more similar chemical

properties.

28.9 X-Ray Spectra and Atomic Number

The effective charge that an electron sees is

the charge on the nucleus shielded by inner

electrons. Only the electrons in the first level

see the entire nuclear charge.

28.9 X-Ray Spectra and Atomic Number

The energy of a level is proportional to Z2, so

the wavelengths corresponding to transitions to

the n 1 state in high-Z atoms are in the X-ray

range.

28.9 X-Ray Spectra and Atomic Number

Inner electrons can be ejected by high-energy

electrons. The resulting X-ray spectrum is

characteristic of the element.

This example is for molybdenum.

28.9 X-Ray Spectra and Atomic Number

Measurement of these spectra allows determination

of inner energy levels, as well as Z, as the

wavelength of the shortest X-rays is inversely

proportional to Z2.

28.9 X-Ray Spectra and Atomic Number

The continuous part of the X-ray spectrum comes

from electrons that are decelerated by

interactions within the material, and therefore

emit photons. This radiation is called

bremsstrahlung (braking radiation).

28.10 Fluorescence and Phosphorescence

If an electron is excited to a higher energy

state, it may emit two or more photons of longer

wavelength as it returns to the lower level.

28.10 Fluorescence and Phosphorescence

Fluorescence occurs when the absorbed photon is

ultraviolet and the emitted photons are in the

visible range.

28.10 Fluorescence and Phosphorescence

Phosphorescence occurs when the electron is

excited to a metastable state it can take

seconds or more to return to the lower state.

Meanwhile, the material glows.

28.11 Lasers

A laser produces a narrow, intense beam of

coherent light. This coherence means that, at a

given cross section, all parts of the beam have

the same phase.

The top figure shows absorption of a photon. The

bottom picture shows stimulated emission if the

atom is already in the excited state, the

presence of another photon of the same frequency

can stimulate the atom to make the transition to

the lower state sooner. These photons are in

phase.

28.11 Lasers

- To obtain coherent light from stimulated

emission, two conditions must be met - Most of the atoms must be in the excited state

this is called an inverted population.

28.11 Lasers

2. The higher state must be a metastable state,

so that once the population is inverted, it stays

that way. This means that transitions occur

through stimulated emission rather than

spontaneously.

28.11 Lasers

The laser beam is narrow, only spreading due to

diffraction, which is determined by the size of

the end mirror.

An inverted population can be created by exciting

electrons to a state from which they decay to a

metastable state. This is called optical pumping.

28.11 Lasers

A metastable state can also be created through

interactions between two sets of atoms, such as

in a helium-neon laser.

28.11 Lasers

Lasers are used for a wide variety of

applications surgery, machining, surveying,

reading bar codes, CDs, and DVDs, and so on. This

diagram shows how a CD is read.

28.12 Holography

Holograms are created using the coherent light of

a laser. The beam is split, allowing the film to

record both the intensity and the relative phase

of the light. The resulting image, when

illuminated by a laser, is three-dimensional.

28.12 Holography

White-light holograms are made with a laser but

can be viewed in ordinary light. The emulsion is

thick, and contains interference patterns that

make the image somewhat three-dimensional.

Summary of Chapter 28

- Quantum mechanics is the basic theory at the

atomic level it is statistical rather than

deterministic - Heisenberg uncertainty principle

- Electron state in atom is specified by four

numbers, n, l, ml, and ms

Summary of Chapter 28

- n, the principal quantum number, can have any

integer value, and gives the energy of the level - l, the orbital quantum number, can have values

from 0 to n 1 - ml, the magnetic quantum number, can have values

from l to l - ms, the spin quantum number, can be ½ or -½
- Energy levels depend on n and l, except in

hydrogen. The other quantum numbers also result

in small energy differences.

Summary of Chapter 28

- Pauli exclusion principle no two electrons in

the same atom can be in the same quantum state - Electrons are grouped into shells and subshells
- Periodic table reflects shell structure
- X-ray spectrum can give information about inner

levels and Z of high-Z atoms