Early Quantum Theory and Models of the Atom Chapter 27

The revolution of the quantum theory took almost three decades to develop.The revolution of the quantum theory took almost three decades to develop. 1890s the discovery of the electron marked the beginning of modern physics1890s the discovery of the electron marked the beginning of modern physics 1900 Planck’s quantum hypothesis1900 Planck’s quantum hypothesis Mid 1920’s theory of quantum mechanics of Schrodinger and Heisenberg which explain the structure of matterMid 1920’s theory of quantum mechanics of Schrodinger and Heisenberg which explain the structure of matter

27-1 Discovery and Properties of the Electron Apparatus-glass tube fitted with electrodes and evacuated so only a small amount of gas remained (rarefied gases)Apparatus-glass tube fitted with electrodes and evacuated so only a small amount of gas remained (rarefied gases) High voltage applied to electrodesHigh voltage applied to electrodes Dark space extended outward from cathode (negative) toward opposite end of tubeDark space extended outward from cathode (negative) toward opposite end of tube

Opposite end of tube would glowOpposite end of tube would glow Screens were placed in the middle of the tube that restricted the glow to a tiny spotScreens were placed in the middle of the tube that restricted the glow to a tiny spot Something was being emitted by the cathode and the “something” traveled across to the opposite endSomething was being emitted by the cathode and the “something” traveled across to the opposite end The “somethings” were named cathode raysThe “somethings” were named cathode rays

What are the “somethings”What are the “somethings” They could be deflected to one side by an electric field or magnetic field.They could be deflected to one side by an electric field or magnetic field. This suggested charged particles. The direction of deflection suggested negative particles.This suggested charged particles. The direction of deflection suggested negative particles. The path of the cathode rays slightly glowed in certain rarefied gasesThe path of the cathode rays slightly glowed in certain rarefied gases

Charge to Mass Ratio 1897 J.J. Thomson was able to directly measure the e/m ration. Until then it was just estimated.J.J. Thomson was able to directly measure the e/m ration. Until then it was just estimated. He used a cathode ray tube that produced an electric field and magnetic field.He used a cathode ray tube that produced an electric field and magnetic field. When only the electric field was present the upper plate became positive and the cathode rays deflected upWhen only the electric field was present the upper plate became positive and the cathode rays deflected up

When only an inward magnetic field existed the cathode rays deflected downwardWhen only an inward magnetic field existed the cathode rays deflected downward Observations follow the path of a negative particleObservations follow the path of a negative particle So F mag =evBSo F mag =evB And F=mv 2 /r for a curved pathAnd F=mv 2 /r for a curved path evB = mv 2 /revB = mv 2 /r e/m=v/Bre/m=v/Br Radius of curvature, r, and magnetic field, B, can be measuredRadius of curvature, r, and magnetic field, B, can be measured Velocity, v, can be foundVelocity, v, can be found

The ratio e/m can be solved for, but not the separate values.The ratio e/m can be solved for, but not the separate values. Today’s accepted value, e/m=1.76 x C/kgToday’s accepted value, e/m=1.76 x C/kg The cathode rays were soon to be called electronsThe cathode rays were soon to be called electrons Robert Millikan, 1909, did his oil drop experiment to accurately determine the charge on an electronRobert Millikan, 1909, did his oil drop experiment to accurately determine the charge on an electron So then the mass could be calculatedSo then the mass could be calculated

27-2 Planck’s Quantum Hypothesis Near the end of the nineteenth century scientists were unable to explain the spectrum of light emitted by hot objects.Near the end of the nineteenth century scientists were unable to explain the spectrum of light emitted by hot objects.

Low temperatures unaware of electromagnetic radiation because of low intensityLow temperatures unaware of electromagnetic radiation because of low intensity Higher temps enough infrared radiation that it can be felt as heatHigher temps enough infrared radiation that 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 with yellow or whitish color, filament of light bulbAt temps above 2000 K objects glow with yellow or whitish color, filament of light bulb As temp increases the electromagnetic radiation emitted increases in intensity and the strongest at higher and higher frequencies.As temp increases the electromagnetic radiation emitted increases in intensity and the strongest at higher and higher frequencies.

Blackbody A body that would absorb all the radiation falling on it so no radiation is reflected and that would make it appear black.A body that would absorb all the radiation falling on it so no radiation is reflected and that would make it appear black. The radiation a blackbody will emit when hot and luminous is called blackbody radiationThe radiation a blackbody will emit when hot and luminous is called blackbody 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 Hypothesis 1900 Max Planck was able to propose a theory that was able to reproduce the graphs.1900 Max Planck was able to propose a theory that was able to reproduce the graphs. He assumed that the energy of the oscillations of atoms cannot have just any valueHe assumed that the energy of the oscillations of atoms cannot have just any value The energy is a multiple of a minimum value related to the frequency of oscillationThe energy is a multiple of a minimum value related to the frequency of oscillation

Planck’s Quantum Hypothesis E=hf or nhfE=hf or nhf E is the energyE is the energy h is Planck’s constanth is Planck’s constant h= x J. sh= x J. s f is the frequencyf is the frequency n is a quantum number (a whole number)n is a quantum number (a whole number) Quantum means discrete amount vs continuousQuantum means discrete amount vs continuous

Energy of oscillator can be hf or 2hf or 3hf, etc…Energy of oscillator can be hf or 2hf or 3hf, etc… But it cannot be in between, continuous energy, as believed for centuriesBut it cannot be in between, continuous energy, as believed for centuries The energy is quantized-it exists only in discrete amounts.The energy is quantized-it exists only in discrete amounts. The smallest being hfThe smallest being hf Similar to gravitational potential energy on stepsSimilar to gravitational potential energy on steps