Quantum Foundations1

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Quantum Foundations - 1

Unless noted otherwise, all images have been taken from:

Physics for Scientists and Engineers, R.D. Knight, 2nd Ed. Copyright 2008

Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Reference: Knight 38.4-38.7


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Classical vs Modern Physics

Classical Physics pre-1900 Physics

Newtonian Mech., inc. Universal gravitation

Electromagnetism via Maxwells Eqns.light identified as em wave phenomenon

Thermodynamics & Classical Statistical Mechanics

+ Rudimentary ideas about atoms


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Crises in physics:

Internal inconsistencies:

Newtonian Mech. vs Maxwells Eqns.(Newtonian addition of velocities in inertial frames; Maxwell: speed of light is thesame in all frames.Either give up Maxwells eqns in all frames or Galileanvelocity addition law. )

Resolution: Einsteins Special Theory of Relativity (1905)

Newtons gravity as action at a distance vs. SpecialRelativity

Resolution: Einsteins General Theory of Relativity (1916)


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Internal inconsistencies (continued):New experimental data:Electron discoveredNucleus discoveredThermal radiation from hot bodiesPhotoelectric effect

Atomic spectra: how do they ariseX-rays discoveredRadioactivity discovered

Resolution: Quantum Mechanics +


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The Situation Today:

Internal inconsistency: Quantum Mech vs General RelativityResolution: Quantum Gravity?Possible framework: String Theory??

Internal inconsistency: Measurement problem in QuantumMechanics..(e.g. Schrodingers Cat Paradox)

Resolution: Environmental decoherence + many worldsinterpretation of Quantum Mech.


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Cathode rays and the discovery of the electron

J.J.Thomson 1987 discovered the electron

Thomson measured the properties of nagative particlesemitted form different metals and found that charge/masswas always the same the electron is a constituent of allmatter.

Millikan 1909 measured the electrons charge


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

Electrical Conduction in Gases

In the 1820s, Faraday showed that current flows through a

low-pressure gas, creating an electric discharge.


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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.


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Thomson & cathode ray tube

Beam of cathode rays emitted from -ve charged cathode.Thomson used crossed E and B fields to study the cathode rays.

The force on an electron in the region of the crossed fields is:

F=e(E-vB)

When there is no deflection: v=E/B


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When there is no deflection: v=E/B

Energy of electron= eVmv =22

1

Where:Vis the potential of the cathodeeis the charge of the electron

Hence ( )V

BE

m

e

2

/2

=

The value of e/m was found to be the same for all cathodematerials (i.e. all metals emit the samecathode)

Conclusion: The electron is a constituent of all matter.


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Millikan & the fundamental unit of charge

Millikan studied charged oil-drops in electric fields.

Can balance the downwardgravitational force on the dropswith an upward electric force:

Eqgmdropdrop

=

E

gmq

dropdrop =

(Drag (air resistance) also played animportant part in Millikans calculations.)

It was found that the drop charges were all integer multiples e:

C106.1 19

=e

kg1011.9 31=emTogether with Thomsons e/m values, we find:


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Rutherford and the discovery of the nucleus

The discovery of charged particles like electrons emanatingfrom atoms, and the fact that atoms emitted em radiation,strongly suggested that atoms were composed of charged

particles. However, atoms were electrically neutral overall # +ve charges = # -ve charges

Thomsons Plum Pudding model:

Early model of the atom.Electrons embedded in asphere of positive charge.


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Rutherford and the Discovery of the Nucleus

In 1909 Geiger andMarsden (at Rutherfordssuggestion) set up an

experiment to see if anyalpha particles weredeflected from gold foil atlargeangles.

Not only were alphaparticles deflected at largeangles, but a very fewwere reflected almoststraight backward towardthe source!

Physics for Scientists and Engineers, Knight 2008 Pearson Addison-Wesley


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In PP model, the alpha particles should not be deflected, asthe charge cloud is diffuse.Deflection through large angles suggested that atoms contain

a positive core.


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The atomic nucleus has a diameter of ~ 10-15 m =1 fmThe diameter of the atom is ~ 10-10 m = 1

1 fm

1

Rutherfords nuclear model of the atom = Planetary Model



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Protons and Neutrons

Soon after Rutherfords discovery of the nucleus, +ve charge wasrecognized to be associated with a subatomic particle proton

Since nearly all the mass of an atom is associated with the

nucleus proton is much more massive than electron

Determination of charge/mass ratio of various atoms suggestedthat the nucleus contained something else (in addition to protons).

The neutron was discovered in 1932

Z= Atomic Number = # of protonsN = # of neutronsA= Mass Number = Z + N



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Classical Physics at the Limit

According to Maxwells theory, the orbiting electrons in a Rutherford atomwould emit EM radiation and loose energy. The solution to this problemlies with quantum physics.


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EXAMPLE 38.5 Energy of an electron


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Quantum Foundations1