chapter 38. the end of classical physics - santa rosa...

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 38. The End of Classical PhysicsStudies of the light emitted by gas discharge tubes helped bring classical physics to an end.Chapter Goal: To understand how scientists discovered the properties of atoms and how these discoveries led to the need for a new theory of light and matter.


Topics:• Physics in the 1800s • Faraday • Cathode Rays • J. J. Thomson and the Discovery of the

Electron • Millikan and the Fundamental Unit of Charge • Rutherford and the Discovery of the Nucleus • Into the Nucleus • The Emission and Absorption of Light • Classical Physics at the Limit

Chapter 38. The End of Classical Physics


Physics in the 1800s

In 1800 Volta invented the battery, and then immediately discovered that an electric current through water decomposes the water into hydrogen and oxygen, a process called electrolysis.


Electrical Conduction in Gases

In the 1820s, Faraday showed that1. Current flows through a low-pressure gas, creating an

electric discharge.2. The color of the discharge depends on the type of gas in

the tube.3. Regardless of the type of gas, there is a separate, constant

glow around the cathode. (Due to nitrogen in air.)


Check out these animations:

• http://highered.mcgraw-hill.com/sites/0072512644/student_view0/chapter2/animations_center.html


Cathode Rays

In the 1850s it was found that a solid object sealed inside a Faraday tube casts a shadow on the glass wall. This discovery suggested that the cathode emits rays of some form that travel in straight lines but are easily blocked by solid objects. These rays were dubbed cathode rays. We now know that cathode rays are high speed electrons.


The TOTAL FORCEElectric & Magnetic Fields

The Electric Force acts parallel to theElectric Field.

The Magnetic Force acts perpendicular to the Magnetic Field and the velocity.

q q= + ×F E v B


Cathode Ray TubeElectric Force makes the Electron gun.

Magnetic Force directs the beam.

Cathode TV has 3 electron guns, one for each color RGB which scan 525 times in 1/30 of a second.


• Used when all the particles need to move with the same velocity

• A uniform electric field is perpendicular to a uniform magnetic field

• When the force due to the electric field is equal but opposite to the force due to the magnetic field, the particle moves in a straight line

• This occurs for velocities of value v = E / B

• Only those particles with the given speed will pass through the two fields undeflected

• The magnetic force exerted on particles moving at speed greater than this is stronger than the electric field and the particles will be deflected upward

• Those moving more slowly will be deflected downward

Velocity Selector


Millikan and the Fundamental Unit of Charge• Millikan observed oil droplets in an

electric field. • He found that some of his droplets were

positively charged and some negatively charged, but all had charges that were integer multiples of a certain minimum charge value.

• That value, the fundamental unit of charge that we now call e, is measured to be

• We can then combine the measured e with the measured charge-to-mass ratio to find that the mass of the electron is


Millikan Oil-Drop Experiment – Experimental Set-Up

PLAYACTIVE FIGURE


Millikan Oil-Drop Experiment

• Robert Millikan measured e, the magnitude of the elementary charge on the electron

• He also demonstrated the quantized nature of this charge

• Oil droplets pass through a small hole and are illuminated by a light


Oil-Drop Experiment

• With no electric field between the plates, the gravitational force and the drag force (viscous) act on the electron

• The drop reaches terminal velocity with


Oil-Drop Experiment

• When an electric field is set up between the plates– The upper plate has a

higher potential• The drop reaches a new

terminal velocity when the electrical force equals the sum of the drag force and gravity


Oil-Drop Experiment

• The drop can be raised and allowed to fall numerous times by turning the electric field on and off

• After many experiments, Millikan determined:– q = ne where n = 0, -1, -2, -3, …– e = 1.60 x 10-19 C

• This yields conclusive evidence that charge is quantized

• Use the active figure to conduct a version of the experiment


EXAMPLE 38.2 Suspending an oil drop

QUESTION:


EXAMPLE 38.2 Suspending an oil drop


Thomson’s Crossed-Field Experiment

• In 1895 Thomson measured the deflection of cathode-ray particles by both a magnetic and electric field.

• Parallel-plate electrodes and the poles of a magnet were placed so that the electric and magnetic fields were perpendicular to each other, thus creating what came to be known as a crossed-field experiment.

• Thomson was the first to measure the charge-to-mass ratio q/m of cathode rays (electrons).

• q/m = 1.76 × 1011 C/kg


Joseph John Thomson“Plum Pudding” Model 1904

Received Nobel Prize in 1906


1911: Rutherford’s Planetary Model of the Atom

(Couldn’t explain the stability or spectra of atoms.)

•A beam of positively charged alpha particles hit and are scattered from a thin foil target.

•Large deflections could not be explained by Thomson’s pudding model.


Rutherford and the Discovery of the Nucleus• In 1896 Rutherford’s

experiment was set up to see if any alpha particles were deflected from gold foil at large angles.

• Not only were alpha particles deflected at large angles, but a very few were reflected almost straight backward toward the source!


Classical Physics at the LimitWHY IS MATTER (ATOMS) STABLE?


Protons repel each other!How is an Atomic Nucleus Stable?


Strong Force is STRONGER than the Coulomb Force over short distances: Short Range Force

~ 100Strong CoulombF F

Over a range of 10-15 m.


Why are Nuclei Not Stable?Why do Atoms Decay?

As nuclear size increases, the distance between nucleons increases and the strong force becomes too weak to overcome the Coulomb electrical repulsion.

The nucleus is unstable and can decay.


Atomic Notation

AZ X

Atomic Mass NumberA = # protons + neutrons

Atomic #

1 3 2381 1 92H, H, U

Atomic NumberZ = # protons

Neutron Number NN = # neutronsN = A - Z


If Helium loses a proton, it becomes a different element

If Helium loses one of its neutrons, it becomes an isotope

Isotopes and Elements

pnn

e

3He

ppn

e

e3H =T


All Elements Have IsotopesSame # of protons - different # of neutronsAtomic Mass of an Element is an average of all Isotopes

Isotopes have the same chemistry as the atom.This is why radioactive isotopes can be so dangerous.

The body doesn’t see the difference between water made with hydrogen and water made with tritium.


Into the Nucleus• The atomic number Z of an element describes the

number of protons in the nucleus. Elements are listed in the periodic table by their atomic number.

• There are a range of neutron numbers N that happily form a nucleus with Z protons, creating a series of nuclei having the same Z-value but different masses. Such a series of nuclei are called isotopes.

• An atom’s mass number A is defined to be A = Z + N. It is the total number of protons and neutrons in a nucleus.

• The notation used to label isotopes is AZ, where the mass number A is given as a leading superscript. The proton number Z is not specified by an actual number but, equivalently, by the chemical symbol for that element.


Carbon is the 6th element in the periodic table. How many electrons are there in a C++ ion?

A. 12B. 2C. 4D. 6E. 8


A. 12B. 2C. 4D. 6E. 8

Carbon is the 6th element in the periodic table. How many electrons are there in a C++ ion?


Carbon is the 6th element in the periodic table. How many neutrons are there in a nucleus of the isotope 14C?

A. 12B. 2C. 4D. 6E. 8


A. 12B. 2C. 4D. 6E. 8

Carbon is the 6th element in the periodic table. How many neutrons are there in a nucleus of the isotope 14C?


The Electron Volt

• Consider an electron accelerating (in a vacuum) from rest across a parallel plate capacitor with a 1.0 V potential difference.

• The electron’s kinetic energy when it reaches the positive plate is 1.60 × 10−19 J.

• Let us define a new unit of energy, called the electron volt, as 1 eV = 1.60 × 10−19 J.


EXAMPLE 38.5 Energy of an electron

QUESTION:


EXAMPLE 38.5 Energy of an electron


The Emission and Absorption of Light

Hot, self-luminous objects, such as the sun or an incandescent lightbulb, SOLIDS, form a rainbow-like continuous spectrum in which light is emitted at every possible wavelength. The figure shows a continuous spectrum.


Why this shape? Why the drop?


Blackbody Radiation• A black body is an ideal system that

absorbs all radiation incident on it• The electromagnetic radiation emitted by a

black body is called blackbody radiation

c


Blackbody Experiment Results• The total power of the radiation emitted from the

surface increases with temperature – Stefan’s law: P = σAeT4

– P is the power and σ is the Stefan-Boltzmann constant: σ = 5.670 x 10-8 W / m2 . K4 (0<e < 1, for a blackbody, e = 1)

• The peak of the wavelength distribution shifts to shorter wavelengths as the temperature increases– Wien’s displacement law (T must be in kelvin):


Intensity of Blackbody Radiation

• The intensity increases with increasing temperature

• The amount of radiation emitted increases with increasing temperature– The area under the curve

• The peak wavelength decreases with increasing temperature

• Combining gives the Rayleigh-Jeans law:

I = P/A = σT4

( )I , ~ 41λ Tλ


EXAMPLE 38.7 Finding peak wavelengths

QUESTIONS:


EXAMPLE 38.7 Finding peak wavelengths


Intensity of Blackbody Radiation

Combining gives the Rayleigh-Jeans law:

I = P/A = σT4

( )I , ~ 41λ Tλ


Problems with the Wein’s World

• At short wavelengths, there was a major disagreement between the Rayleigh-Jeans law and experiment

• This mismatch became known as the ultraviolet catastrophe– You would have infinite

energy as the wavelength approaches zero

( )I , ~ 41λ Tλ


Incandescent Light Bulb


Continuous vs Discreet

This is a continuous spectrum of colors: all colors are present.

This is a discreet spectrum of colors: only a few are present.


The Emission and Absorption of Light

The light emitted by one of Faraday’s gas discharge tubes contains only certain discrete, individual wavelengths. Such a spectrum is called a discrete spectrum. Each wavelength in a discrete spectrum is called a spectral line because of its appearance in photographs such as the one shown.


Kirkoff’s Rules


Absorption Spectrum of Hydrogen Gas


Kirkoff’s Rules for Spectra: 1859

Bunsen

German physicist who developed the spectroscope and the science of emission spectroscopy with Bunsen.

Kirkoff

* Rule 1 : A hot and opaque solid, liquid or highly compressed gas emits a continuous spectrum.* Rule 2 : A hot, transparent gas produces an emission spectrum with bright lines. * Rule 3 : If a continuous spectrum passes through a gas at a lower temperature, the transparent cooler gas generates dark absorption lines.


Compare absorption lines in a source with emission lines found in the laboratory!

Kirchhoff deduced that elements were present in the atmosphere of the Sun and were absorbing their characteristic wavelengths, producing the absorption lines in the solar spectrum. He published in 1861 the first atlas of the solar spectrum, obtained with a prism ; however, these wavelengths were not very precise : the dispersion of the prism was not linear at all.


Anders Jonas Ångström 1869

Ångström measured the wavelengths on the four visible lines of the hydrogen spectrum, obtained with a diffraction grating, whose dispersion is linear, and replaced Kirchhoff's arbitrary scale by the wavelengths, expressed in the metric system, using a small unit (10-10 m) with which his name was to be associated.

Line color Wavelengthred 6562.852 Åblue-green 4861.33 Åviolet 4340.47 Åviolet 4101.74 Å


Balmer Series: 1885Johann Balmer found an empirical equation that correctly

predicted the four visible emission lines of hydrogen

H 2 21 1 1

2R

λ n⎛ ⎞= −⎜ ⎟⎝ ⎠

RH is the Rydberg constantRH = 1.097 373 2 x 107 m-1

n is an integer, n = 3, 4, 5,…The spectral lines correspond to different values of n

Johannes Robert Rydberg generalized it in 1888 for all transitions:

Hα is red, λ = 656.3 nmHβ is green, λ = 486.1 nmHγ is blue, λ = 434.1 nmHδ is violet, λ = 410.2 nm


Discrete Spectra

• Not only does low-density gas emit discrete wavelengths, but it also may absorb discrete wavelengths.

• Every wavelength absorbed by the gas is also emitted, but not every emitted wavelength is absorbed.

• The wavelengths in the hydrogen spectrum can be represented by the Balmer formula


•Cosmological Redshift: Expanding Universe•Stellar Motions: Rotations and Radial Motions•Solar Physics: Surface Studies and Rotations•Gravitational Redshift: Black Holes & Lensing•Exosolar Planets via Doppler Wobbler

Everything we know about the Universe is based on SPECTRA!


Doppler Shift for LightDoppler Shift for LightSpectral lines shift due to the relative motion between the source and the

observer


• Red Shift: Moving Away• Blue Shift: Moving Toward


V = Ho dThe Universe is Expanding

1 Megaparsec = 3.26 million light years

Ho = 77 km/s/Mpc


Dispersion: Diffraction GratingsHow does dispersion with a grating compare with a prism?

Longer wavelength light is bent more with a grating.Shorter wavelength light is bent more with a prism.

sind mθ λ=


Hydrogen Spectra

http://www.assumption.edu/users/bniece/CHE131/LineSpectra/HiResolution/H2.pdf


Helium Spectra

http://www.assumption.edu/users/bniece/CHE131/LineSpectra/HiResolution/He.pdf


Mercury Spectra


Neon Spectrum

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