Loading...

PPT – Atomic Physics PowerPoint presentation | free to download - id: 573bcf-MzJhY

The Adobe Flash plugin is needed to view this content

Chapter 28

- Atomic Physics

Plum Pudding Model of the Atom

- J. J. Thomsons Plum Pudding model of the atom
- Electrons embedded throughout the a volume of

positive charge - A change from Newtons model of the atom as a

tiny, hard, indestructible sphere

Scattering Experiments

- The source was a naturally radioactive material

that produced alpha particles - Most of the alpha particles passed though the

foil - A few deflected from their original paths
- Some even reversed their direction of travel

Planetary Model of the Atom

- Based on results of thin foil scattering

experiments, Rutherfords Planetary model of the

atom - Positive charge is concentrated in the center of

the atom, called the nucleus - Electrons orbit the nucleus like planets orbit

the sun

Difficulties with the Rutherford Model

- Atoms emit certain discrete characteristic

frequencies of electromagnetic radiation but the

Rutherford model is unable to explain this

phenomena - Rutherfords electrons are undergoing a

centripetal acceleration and so should radiate

electromagnetic waves of the same frequency - The radius should steadily decrease as this

radiation is given off - The electron should eventually spiral into the

nucleus, but it doesnt

Emission Spectra

- A gas at low pressure and a voltage applied to it

emits light characteristic of the gas - When the emitted light is analyzed with a

spectrometer, a series of discrete bright lines

emission spectrum is observed - Each line has a different wavelength and color

Emission Spectrum of Hydrogen

- The wavelengths of hydrogens spectral lines can

be found from - RH 1.097 373 2 x 107 m-1 is the Rydberg

constant and n is an integer, n 1, 2, 3, - The spectral lines correspond to different values

of n - n 3, ? 656.3 nm
- n 4, ? 486.1 nm

Absorption Spectra

- An element can also absorb light at specific

wavelengths - An absorption spectrum can be obtained by passing

a continuous radiation spectrum through a vapor

of the gas - Such spectrum consists of a series of dark lines

superimposed on the otherwise continuous spectrum - The dark lines of the absorption spectrum

coincide with the bright lines of the emission

spectrum

Chapter 28Problem 6

- In a Rutherford scattering experiment, an

a-particle (charge 2e) heads directly toward a

gold nucleus (charge 79e). The a-particle had

a kinetic energy of 5.0 MeV when very far (r ? 8)

from the nucleus. Assuming the gold nucleus to be

fixed in space, determine the distance of closest

approach.

The Bohr Theory of Hydrogen

- In 1913 Bohr provided an explanation of atomic

spectra that includes some features of the

currently accepted theory - His model was an attempt to explain why the atom

was stable and included both classical and

non-classical ideas

The Bohr Theory of Hydrogen

- The electron moves in circular orbits around the

proton under the influence of the Coulomb force

of attraction, which produces the centripetal

acceleration - Only certain electron orbits are stable
- In these orbits electrons do not emit energy in

the form of electromagnetic radiation - Therefore, the energy of the atom
- remains constant and classical
- mechanics can be used to describe
- the electrons motion

The Bohr Theory of Hydrogen

- Radiation is emitted when the electrons jump

(not in a classical sense) from a more energetic

initial state to a lower state - The frequency emitted in the jump is related to

the change in the atoms energy Ei Ef h ƒ - The size of the allowed electron orbits is

determined by a quantization condition imposed on

the electrons orbital angular momentum - me v r n h where n 1, 2, 3, h h / 2 p

Radii and Energy of Orbits

Radii and Energy of Orbits

Radii and Energy of Orbits

- The radii of the Bohr orbits are quantized
- When n 1, the orbit has the smallest radius,

called the Bohr radius, ao 0.0529 nm - A general expression for the radius of any orbit

in a hydrogen atom is rn n2 ao

Radii and Energy of Orbits

- The lowest energy state (n 1) is called the

ground state, with energy of 13.6 eV - The next energy level (n 2) has an energy of

3.40 eV - The energies can be compiled in an energy level

diagram with the energy of any orbit of En -

13.6 eV / n2

Energy Level Diagram

Energy Level Diagram

- The value of RH from Bohrs analysis is in

excellent agreement with the experimental value

of the Rydberg constant - A more generalized equation can be
- used to find the wavelengths of any
- spectral lines

Energy Level Diagram

- The uppermost level corresponds to E 0 and n ?

? - The ionization energy energy needed to

completely remove the electron from the atom - The ionization energy for hydrogen
- is 13.6 eV

Chapter 28Problem 18

- A particle of charge q and mass m, moving with a

constant speed v, perpendicular to a constant

magnetic field, B, follows a circular path. If in

this case the angular momentum about the center

of this circle is quantized so that mvr 2nh,

show that the expression for the allowed radii

for the particle are written in the corner, where

n 1, 2, 3, . . .

Chapter 28Problem 24

- Two hydrogen atoms collide head-on and end up

with zero kinetic energy. Each then emits a

121.6-nm photon (n 2 to n 1 transition). At

what speed were the atoms moving before the

collision?

Modifications of the Bohr Theory Elliptical

Orbits

- Sommerfeld extended the results to include

elliptical orbits - Retained the principal quantum number, n, which

determines the energy of the allowed states - Added the orbital quantum number, l, ranging from

0 to n-1 in integer steps - All states with the same principle quantum
- number are said to form a shell, whereas the
- states with given values of n and l are said
- to form a subshell

Modifications of the Bohr Theory Elliptical

Orbits

Modifications of the Bohr Theory Zeeman Effect

- Another modification was needed to account for

the Zeeman effect splitting of spectral lines in

a strong magnetic field, indicating that the

energy of an electron is slightly modified when

the atom is immersed in a magnetic field - A new quantum number, m l, called the orbital

magnetic quantum number, had to be introduced - m l can vary from - l to l in integer steps

Quantum Number Summary

- The values of n can range from 1 to ? in integer

steps - The values of l can range from 0 to n-1 in

integer steps - The values of m l can range from -l to l in

integer steps

Modifications of the Bohr Theory Fine Structure

- High resolution spectrometers show that spectral

lines are, in fact, two very closely spaced

lines, even in the absence of a magnetic field - This splitting is called fine structure
- Another quantum number, ms, called the spin

magnetic quantum number, was introduced to

explain the fine structure

Spin Magnetic Quantum Number

- It is convenient to think of the electron as

spinning on its axis (the electron is not

physically spinning) - There are two directions for the spin spin up,

ms ½ spin down, ms - ½ - There is a slight energy difference between the

two spins and this accounts for the doublet in

some lines - A classical description of electron spin is

incorrect the electron cannot be located

precisely in space, thus it cannot be considered

to be a spinning solid object

de Broglie Waves in the Hydrogen Atom

- One of Bohrs postulates was the angular momentum

of the electron is quantized, but there was no

explanation why the restriction occurred - de Broglie assumed that the electron orbit would

be stable only if it contained an integral number

of electron wavelengths

de Broglie Waves in the Hydrogen Atom

- This was the first convincing argument that the

wave nature of matter was at the heart of the

behavior of atomic systems - By applying wave theory to the electrons in an

atom, de Broglie was able to explain the

appearance of integers in Bohrs equations as a

natural consequence of standing wave patterns

Quantum Mechanics and the Hydrogen Atom

- Schrödingers wave equation was subsequently

applied to hydrogen and other atomic systems -

one of the first great achievements of quantum

mechanics - The quantum numbers and the restrictions placed

on their values arise directly from the

mathematics and not from any assumptions made to

make the theory agree with experiments

Electron Clouds

- The graph shows the solution to the wave equation

for hydrogen in the ground state - The curve peaks at the Bohr radius
- The electron is not confined to a particular

orbital distance from the nucleus - The probability of finding the electron at the

Bohr radius is a maximum

Electron Clouds

- The wave function for hydrogen in the ground

state is symmetric - The electron can be found in a spherical region

surrounding the nucleus - The result is interpreted by viewing the electron

as a cloud surrounding the nucleus - The densest regions of the cloud represent the

highest probability for finding the electron

The Pauli Exclusion Principle

- No two electrons in an atom or in the same

location can ever have the same set of values of

the quantum numbers n, l, m l, and ms - This explains the electronic structure of complex

atoms as a succession of filled energy levels

with different quantum numbers

Filling Shells

- As a general rule, the order that electrons fill

an atoms subshell is - 1) Once one subshell is filled, the next electron

goes into the vacant subshell that is lowest in

energy - 2) Otherwise, the electron would radiate energy

until it reached the subshell with the lowest

energy - 3) A subshell is filled when it holds 2(2l1)

electrons

Filling Shells

The Periodic Table

- The outermost electrons are primarily responsible

for the chemical properties of the atom - Mendeleev arranged the elements according to

their atomic masses and chemical similarities - The electronic configuration of the elements is

explained by quantum numbers and Paulis

Exclusion Principle

The Periodic Table

(No Transcript)

Chapter 28Problem 28

- (a) Construct an energy level diagram for the He

ion, for which Z 2. (b) What is the ionization

energy for He?

Explanation of Characteristic X-Rays

- The details of atomic structure can be used to

explain characteristic x-rays - A bombarding electron collides with an electron

in the target metal that is in an inner shell - If there is sufficient energy, the electron is

removed from the target atom

Explanation of Characteristic X-Rays

- The vacancy created by the lost electron is

filled by an electron falling to the vacancy from

a higher energy level - The transition is accompanied by the emission of

a photon whose energy is equal to the difference

between the two levels

Energy Bands in Solids

- In solids, the discrete energy levels of isolated

atoms broaden into allowed energy bands separated

by forbidden gaps - The separation and the electron population of the

highest bands determine whether the solid is a

conductor, an insulator, or a semiconductor

Energy Bands in Solids

- Sodium example
- Blue represents energy bands occupied by the

sodium electrons when the atoms are in their

ground states, gold represents energy bands that

are empty, and white represents energy gaps - Electrons can have any energy within the allowed

bands and cannot have energies in the gaps

Energy Level Definitions

- The valence band is the highest filled band
- The conduction band is the next higher empty band
- The energy gap has an energy, Eg, equal to the

difference in energy between the top of the

valence band and the bottom of the conduction band

Conductors

- When a voltage is applied to a conductor, the

electrons accelerate and gain energy - In quantum terms, electron energies increase if

there are a high number of unoccupied energy

levels for the electron to jump to - For example, it takes very little
- energy for electrons to jump
- from the partially filled to one of
- the nearby empty states

Insulators

- The valence band is completely full of electrons
- A large band gap separates the valence and

conduction bands - A large amount of energy is needed for an

electron to be able to jump from the valence to

the conduction band - The minimum required energy is Eg

Semiconductors

- A semiconductor has a small energy gap
- Thermally excited electrons have enough energy to

cross the band gap - The resistivity of semiconductors decreases with

increases in temperature - The light-color area in the valence band

represents holes empty states in the valence

band created by electrons that have jumped to the

conduction band

Semiconductors

- Some electrons in the valence band move to fill

the holes and therefore also carry current - The valence electrons that fill the holes leave

behind other holes - It is common to view the conduction process in

the valence band as a flow of positive holes

toward the negative electrode applied to the

semiconductor

Semiconductors

- An external voltage is supplied
- Electrons move toward the positive electrode
- Holes move toward the negative electrode
- There is a symmetrical current process in a

semiconductor

Doping in Semiconductors

- Doping is the adding of impurities to a

semiconductor (generally about 1 impurity atom

per 107 semiconductor atoms) - Doping results in both the band structure and the

resistivity being changed

n-type Semiconductors

- Donor atoms are doping materials that contain one

more electron than the semiconductor material - This creates an essentially free electron with an

energy level in the energy gap, just below the

conduction band - Only a small amount of thermal energy is needed

to cause this electron to move into the

conduction band

p-type Semiconductors

- Acceptor atoms are doping materials that contain

one less electron than the semiconductor material - A hole is left where the missing electron would

be - The energy level of the hole lies in the energy

gap, just above the valence band - An electron from the valence band has enough

thermal energy to fill this impurity level,

leaving behind a hole in the valence band

A p-n Junction

- A p-n junction is formed when a p-type

semiconductor is joined to an n-type - Three distinct regions exist a p region, an n

region, and a depletion region - Mobile donor electrons from the n side nearest

the junction diffuse to the p side, leaving

behind immobile positive ions

A p-n Junction

- At the same time, holes from the p side nearest

the junction diffuse to the n side and leave

behind a region of fixed negative ions - The resulting depletion region is depleted of

mobile charge carriers - There is also an electric field in this region

that sweeps out mobile charge carriers to keep

the region truly depleted

Diode Action

- The p-n junction has the ability to pass current

in only one direction - When the p-side is connected to a positive

terminal, the device is forward biased and

current flows - When the n-side is connected to the positive

terminal, the device is reverse biased and a

very small reverse current results

- Answers to Even Numbered Problems
- Chapter 28
- Problem 34
- 4
- 7

Answers to Even Numbered Problems Chapter 28

Problem 36 Use the lecture notes

Answers to Even Numbered Problems Chapter 28

Problem 44 137

- Answers to Even Numbered Problems
- Chapter 28
- Problem 52
- 135 eV
- 10 times the magnitude of the ground state

energy of hydrogen