Early Quantum Theory Early Quantum Theory and Models of the Atomand Models of the Atom

Chapter 27Chapter 27

• The revolution of the quantum The revolution of the quantum theory took almost three decades theory took almost three decades to develop.to develop.

• 1890s the discovery of the electron 1890s the discovery of the electron marked the beginning of modern marked the beginning of modern physicsphysics

• 1900 Planck’s quantum hypothesis1900 Planck’s quantum hypothesis• Mid 1920’s theory of quantum Mid 1920’s theory of quantum

mechanics of Schrodinger and mechanics of Schrodinger and Heisenberg which explain the Heisenberg which explain the structure of matterstructure of matter

27-1 Discovery and 27-1 Discovery and Properties of the ElectronProperties of the Electron

• Apparatus-glass tube fitted with Apparatus-glass tube fitted with electrodes and evacuated so only electrodes and evacuated so only a small amount of gas remained a small amount of gas remained (rarefied gases)(rarefied gases)

• High voltage applied to electrodesHigh voltage applied to electrodes• Dark space extended outward from Dark space extended outward from

cathode (negative) toward cathode (negative) toward opposite end of tubeopposite end of tube

• Opposite end of tube would glowOpposite end of tube would glow• Screens were placed in the middle Screens were placed in the middle

of the tube that restricted the glow of the tube that restricted the glow to a tiny spotto a tiny spot

• Something was being emitted by Something was being emitted by the cathode and the “something” the cathode and the “something” traveled across to the opposite endtraveled across to the opposite end

• The “somethings” were named The “somethings” were named cathode rayscathode rays

• What are the “somethings”What are the “somethings”• They could be deflected to one side They could be deflected to one side

by an electric field or magnetic field.by an electric field or magnetic field.• This suggested charged particles. This suggested charged particles.

The direction of deflection suggested The direction of deflection suggested negative particles.negative particles.

• The path of the cathode rays slightly The path of the cathode rays slightly glowed in certain rarefied gasesglowed in certain rarefied gases

Charge to Mass Ratio 1897Charge to Mass Ratio 1897

• J.J. Thomson was able to directly J.J. Thomson was able to directly measure the e/m ration. Until then measure the e/m ration. Until then it was just estimated.it was just estimated.

• He used a cathode ray tube that He used a cathode ray tube that produced an electric field and produced an electric field and magnetic field.magnetic field.

• When only the electric field was When only the electric field was present the upper plate became present the upper plate became positive and the cathode rays positive and the cathode rays deflected updeflected up

• When only an inward magnetic When only an inward magnetic field existed the cathode rays field existed the cathode rays deflected downwarddeflected downward

• Observations follow the path of a Observations follow the path of a negative particlenegative particle

• So FSo Fmagmag=evB=evB• And F=mvAnd F=mv22/r for a curved path/r for a curved path• evB = mvevB = mv22/r/r• e/m=v/Bre/m=v/Br• Radius of curvature, r, and Radius of curvature, r, and

magnetic field, B, can be magnetic field, B, can be measuredmeasured

• Velocity, v, can be foundVelocity, v, can be found

• The ratio e/m can be solved for, but not The ratio e/m can be solved for, but not the separate values.the separate values.

• Today’s accepted value, e/m=1.76 x 10Today’s accepted value, e/m=1.76 x 101111 C/kgC/kg

• The cathode rays were soon to be called The cathode rays were soon to be called electronselectrons

• Robert Millikan, 1909, did his oil drop Robert Millikan, 1909, did his oil drop experiment to accurately determine the experiment to accurately determine the charge on an electroncharge on an electron

• So then the mass could be calculatedSo then the mass could be calculated

27-2 Planck’s Quantum 27-2 Planck’s Quantum HypothesisHypothesis

• Near the end of the nineteenth Near the end of the nineteenth century scientists were unable to century scientists were unable to explain the spectrum of light explain the spectrum of light emitted by hot objects.emitted by hot objects.

• Low temperatures unaware of Low temperatures unaware of electromagnetic radiation because of electromagnetic radiation because of low intensitylow intensity

• Higher temps enough infrared radiation Higher temps enough infrared radiation that it can be felt as heatthat it can be felt as heat

• At higher temps yet object glow, burnerAt higher temps yet object glow, burner• At temps above 2000 K objects glow At temps above 2000 K objects glow

with yellow or whitish color, filament of with yellow or whitish color, filament of light bulblight bulb

• As temp increases the electromagnetic As temp increases the electromagnetic radiation emitted increases in intensity radiation emitted increases in intensity and the strongest at higher and higher and the strongest at higher and higher frequencies.frequencies.

BlackbodyBlackbody

• A body that would absorb all the A body that would absorb all the radiation falling on it so no radiation falling on it so no radiation is reflected and that radiation is reflected and that would make it appear black.would make it appear black.

• The radiation a blackbody will emit The radiation a blackbody will emit when hot and luminous is called when hot and luminous is called blackbody radiationblackbody radiation

This figure shows blackbody radiation curves for three different temperatures. Note that frequency increases to the left. Blue end of spectrum is weaker at low temps. Objects glow with a red color around 1000 K.

Temperature of the Sun

Planck’s Quantum Planck’s Quantum HypothesisHypothesis

• 1900 Max Planck was able to propose 1900 Max Planck was able to propose a theory that was able to reproduce a theory that was able to reproduce the graphs.the graphs.

• He assumed that the energy of the He assumed that the energy of the oscillations of atoms cannot have just oscillations of atoms cannot have just any valueany value

• The energy is a multiple of a minimum The energy is a multiple of a minimum value related to the frequency of value related to the frequency of oscillationoscillation

Planck’s Quantum Planck’s Quantum HypothesisHypothesis

• E=hf or nhfE=hf or nhf• E is the energy E is the energy • h is Planck’s constanth is Planck’s constant• h= 6.626 x 10h= 6.626 x 10-34-34 J J..ss• f is the frequencyf is the frequency• n is a quantum number (a whole n is a quantum number (a whole

number)number)• Quantum means discrete amount vs Quantum means discrete amount vs

continuouscontinuous

• Energy of oscillator can be hf or Energy of oscillator can be hf or 2hf or 3hf, etc…2hf or 3hf, etc…

• But it cannot be in between, But it cannot be in between, continuous energy, as believed for continuous energy, as believed for centuriescenturies

• The energy is quantized-it exists The energy is quantized-it exists only in discrete amounts.only in discrete amounts.

• The smallest being hfThe smallest being hf• Similar to gravitational potential Similar to gravitational potential

energy on stepsenergy on steps