presentation lesson 27 quantum physicsstemgarage.org/toolbox_physics/physics...
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SCIENCE – PHYSICSSTEM GARAGE
Quantum Physics
Chin-‐Sung Lin
SCIENCE – PHYSICSSTEM GARAGE
The Model of Atom
SCIENCE – PHYSICSSTEM GARAGE
The Planetary Model of Atom
• Niels Bohr’s model
• Posi7ve charge is in the center of the atom (nucleus )
• Atom has zero net charge
• Electrons orbit the nucleus like planets orbit the sun
• ABrac7ve Coulomb force plays role of gravity
SCIENCE – PHYSICSSTEM GARAGE
The Planetary Model of Atom • Circular mo7on of orbi7ng electrons causes them to emit
electromagne7c radia7on with frequency equal to orbital frequency, and carries away energy from the electron
– Electron predicted to con7nually lose energy – The electron would eventually spiral into the nucleus
However most atoms are stable!
SCIENCE – PHYSICSSTEM GARAGE
The Planetary Model of Atom • Experimentally, atoms do emit electromagne7c
radia7on, but not just any radia7on!
• Each atom has its own ‘fingerprint’ of different light frequencies that it emits
Hydrogen
Mercury
Wavelength (nm)
400 nm 500 nm 600 nm 700 nm
SCIENCE – PHYSICSSTEM GARAGE
The Planetary Model of Atom
n = 3, λ = 656.3 nm
Hydrogen
n = 4, λ = 486.1 nm
n=3 n=4
€
1λm
= RH122
−1n2
$
% &
'
( )
• The Balmer Series of emission lines empirically given by
€
Rydberg constant : RH =1.097 ×107m−1
SCIENCE – PHYSICSSTEM GARAGE
• One electron orbits around one proton and only certain orbits are stable
• Radia7on emiBed only when electron jumps from one stable orbit to another
• Here, the emiBed photon has an energy of E ini1al – E final
Eini1al
EfinalPhoton
The Planetary Model of Atom
SCIENCE – PHYSICSSTEM GARAGE
• Hydrogen emits only photons of a par7cular wavelength, frequency
• Photon energy = hf, so this means a par7cular energy
The Planetary Model of Atom
SCIENCE – PHYSICSSTEM GARAGE
• Energy is quan7zed
Zero energy
n=1
n=2
n=3 n=4
€
E1 = −13.612 eV
€
E2 = −13.622 eV
€
E3 = −13.632 eV
Energy axis
The Planetary Model of Atom
SCIENCE – PHYSICSSTEM GARAGE
Photon is emiBed when electron drops from one quantum state to another
Zero energy
n=1
n=2
n=3 n=4
€
E1 = −13.612 eV
€
E2 = −13.622 eV
€
E3 = −13.632 eV
n=1
n=2
n=3 n=4
€
E1 = −13.612 eV
€
E2 = −13.622 eV
€
E3 = −13.632 eV
Absorbing a photon of correct energy makes electron jump to higher quantum state.
Photon absorbed hf=E2-‐E1
Photon emiBed hf=E2-‐E1
The Planetary Model of Atom
SCIENCE – PHYSICSSTEM GARAGE
The Planetary Model of Atom • A useful model of the atom must be consistent with a
model for light, for most of what we know about atoms we learn from the light and other radia7ons they emit
• Most light has its source in the mo7on of electrons within the atom
SCIENCE – PHYSICSSTEM GARAGE
Models of Light
SCIENCE – PHYSICSSTEM GARAGE
The Model of Light • Two primary models of light: the par7cle model and the
wave model
SCIENCE – PHYSICSSTEM GARAGE
The Model of Light • Isaac Newton believed in a par7cle model of light
• Chris7an Huygens believed that light was a wave
• Thomas Young demonstrated the wave property of light – Interference
• James Clerk Maxwell proposed that light is a part of broader electromagne7c wave spectrum
• Heinrich Hertz produced radio wave as Maxwell’s predic7on
• Albert Einstein resurrected the par7cle theory of light
SCIENCE – PHYSICSSTEM GARAGE
Light Quanta • Max Planck believed that light existed as con7nuous waves.
However, he proposed that atoms emit and absorb light in liBle chunks – quanta (pl. of quantum)
• Einstein further proposed that light itself is composed of quanta (now called photons)
• A quantum is an elementary unit (smallest amount) of something
• Mass, electric charge, light, energy, and angular momentum are all quan7zed
• Only a whole number of quanta can exist
SCIENCE – PHYSICSSTEM GARAGE
Light Quanta • Photons have no rest energy
• Photons move at speed of light
• The energy of a photon is its kine7c energy (E)
• The photon’s energy is directly propor7onal to its frequency
• E = hf (h is Planck’s constant) is the smallest amount of energy that can be converted to light of frequency f
• Light is a stream of photons, each with an energy hf
SCIENCE – PHYSICSSTEM GARAGE
Photoelectric Effect
SCIENCE – PHYSICSSTEM GARAGE
Photoelectric Effect
• The photoelectric effect refers to the emission of electrons from the surface of a metal in response to incident light
• Energy is absorbed by electrons within the metal, giving the electrons sufficient energy to be 'knocked' out of the surface of the metal
SCIENCE – PHYSICSSTEM GARAGE
Photoelectric Effect
• Maxwell wave theory of light predicts that the more intense the incident light the greater the average energy carried by an ejected (photoelectric) electron
• Experiment shows that the energies of the emi6ed electrons to be independent of the intensity of the incident radia7on
• Einstein (1905) resolved this paradox by proposing that the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete par7cles, rather than as con7nuous waves
SCIENCE – PHYSICSSTEM GARAGE
Photoelectric Effect
• For a given frequency of the incident radia7on, each photon carried the energy E = hf, where h is Planck's constant and f is the frequency
SCIENCE – PHYSICSSTEM GARAGE
Photoelectric Effect
• Light travels as a wave
• Light interacts with maBer as a stream of par7cles
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles • Images made by a digital camera. In each successive image,
the dim spot of light has been made even dimmer by inser7ng semitransparent absorbers like the 7nted plas7c used in sunglasses
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles • Which model can explain the phenomenon?
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles • If light was a wave, then the absorbers would simply cut down
the wave's amplitude across the whole wavefront
• The digital camera's en7re chip would be illuminated uniformly
• But figures show that some pixels take strong hits while others pick up no energy at all
• Instead of the wave picture, the image that is naturally evoked by the data is something more like a hail of bullets from a machine gun
• Each "bullet" of light apparently carries only a 7ny amount of energy – light is consist of a stream of par7cles
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles
Electron beam is directed toward a crystal
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles
Diffrac7on & interference paBern is observed
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles
• The behavior of a par7cle of maBer (in this case the incident electron) can be described by a wave
• Electrons behave like a wave!
SCIENCE – PHYSICSSTEM GARAGE
Waves vs. Par7cles
• If waves can have par7cle proper7es, cannot par7cles have wave property?
• De Broglie answered this ques7on in 1924
• He suggested that all maBer (electrons, protons, atoms, marbles, cars, and even human) have wave proper7es
• This phenomenon is commonly known as the wave-‐par8cle duality
SCIENCE – PHYSICSSTEM GARAGE
Material Waves
SCIENCE – PHYSICSSTEM GARAGE
Material Waves • All maBer have wave proper7es
• The wavelength of a par7cle is called the de Broglie wavelength
• A 7ny par7cle moving at typical speed has a detectable wavelength
• Objects in our daily life have 7ny wavelengths which are beyond detec7on
SCIENCE – PHYSICSSTEM GARAGE
Wavelength of an Electron
• Need less massive object to show wave effects • Electron is a very light par7cle • Mass of electron = 9.1x10-‐31 kg
• Larger velocity, shorter wavelength • Wavelength depends on mass and velocity
€
λ =hp
=hmv
=6 ×10−34 J • s
9 ×10−31kg( ) × velocity( )
SCIENCE – PHYSICSSTEM GARAGE
Wavelength of a Football
Example: A football’s weight is 0.4 kg and the speed is 30 m/s. Calculate the wavelength of the football
Momentum:
€
mv = 0.4 kg( ) 30 m /s( ) =12 kg • m /s
€
λ =hp
=6.6 ×10−34 J • s
12 kg −m /s= 5.5 ×10−35m = 5.5 ×10−26nm
SCIENCE – PHYSICSSTEM GARAGE
Material Waves
• Example: Calculate the de Broglie wavelength of an electron traveling at 2% the speed of light
SCIENCE – PHYSICSSTEM GARAGE
Material Waves
• Example: Calculate the de Broglie wavelength of an ball traveling at 330 m/s
SCIENCE – PHYSICSSTEM GARAGE
Material Waves
• A beam of electrons behaves like a beam of light, however, the wavelength is typically thousands of 7mes shorter than the wavelength of the visible light
SCIENCE – PHYSICSSTEM GARAGE
Material Waves
• The electron microscope can dis7nguish detail not possible with op7cal microscopes
SCIENCE – PHYSICSSTEM GARAGE
Electron Waves • The Bohr’s model explained the spectra of the element. It
explained why elements emiBed only certain frequencies of light since electrons can only transfer among certain energy levels
• The model failed to explain why electrons only occupied certain energy levels in the atom
• Bohr showed that in such a model the electrons would spiral into the nucleus in about 10-‐10 s, due to electrosta7c aBrac7on
• This can be resolved by viewing electrons as waves instead of par7cles
SCIENCE – PHYSICSSTEM GARAGE
Electron Waves • In 1923, de Broglie, proposed that a way to explain the
discrete energy levels was that electrons behave like waves
• To ‘fit a wave’ around a nucleus is when the wavelength fits the circumference a whole-‐number of 7mes (so called standing waves ), and these states correspond to the observed energy levels of the electrons
SCIENCE – PHYSICSSTEM GARAGE
Electron Waves • The radius of a ground state, n = 1, electron has a
circumference of one standing wave
• The radius of the first excited state, n = 2, has a circumference of two standing waves
SCIENCE – PHYSICSSTEM GARAGE
Electron Waves • Thus, an electron's orbit cannot decay because it is
constrained by its standing wave forms
• Only those radii whose circumferences equaled a mul7ple of the electron's de Broglie wavelength were permiBed
SCIENCE – PHYSICSSTEM GARAGE
Electron Waves • De Broglie’s predic7ons for the electron orbits were quickly
confirmed by experiment and were found to perfectly fit the observed energy levels of electrons in atoms
• De Broglie thus created a new field in physics, the wave mechanics, uni7ng the physics of energy (wave) and maBer (par7cle). For this he won the Nobel Prize in Physics in 1929
SCIENCE – PHYSICSSTEM GARAGE
Rela7ve Sizes of Atoms
SCIENCE – PHYSICSSTEM GARAGE
Rela7ve Sizes of Atoms • The radii of the electron orbits in the Bohr’s atomic model are
determined by the amount of electric charge in the nucleus
• As the posi7ve charge in the nucleus increased, the nega7ve electrons also increased. The inner orbits shrink in size due to stronger electric aBrac7on. However, it won’t shrink as much as expected due to the increasing electrons
• The heavier elements are not much larger in diameter than the lighter elements
• Each element has unique arrangement of electron orbits unique to that element
SCIENCE – PHYSICSSTEM GARAGE
Rela7ve Sizes of Atoms
SCIENCE – PHYSICSSTEM GARAGE
Atomic Energy Levels & Photon Energy
SCIENCE – PHYSICSSTEM GARAGE
• Electron orbits around the nucleus and only certain orbits are stable
• Radia7on emiBed only when electron jumps from one stable orbit to another
• The emiBed photon has an energy E photon = E ini1al – E final
Bohr’s Atomic Model
Eini1al
Efinal
Photon Ephoton
SCIENCE – PHYSICSSTEM GARAGE
• Energy level diagrams on page 3 of your reference table
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• Each atom has a set of discrete energy levels
• Each level has been assigned a quantum number (n)
• An electron transits in hydrogen between quan7zed energy levels
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 4?
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 4?
3 different transi1ons: n = 4 —> n = 3 n = 4 —> n = 2 n = 4 —> n = 1
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 7 ?
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 7 ?
6 different transi1ons
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the energy of photons for those possible transi7ons form n = 4
Energy of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the energy of photons for those possible transi7ons form n = 4
3 possible transi1ons: n = 4 —> n = 3 -‐0.85 eV – (-‐1.51 eV) = 0.66 eV n = 4 —> n = 2 -‐0.85 eV – (-‐3.40 eV) = 2.55 eV n = 4 —> n = 1 !!-‐0.85 eV – (-‐13.6 eV) = 12.75 eV
Energy of Photons
SCIENCE – PHYSICSSTEM GARAGE
• How much energy is required to ionize the Hydrogen atom?
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• How much energy is required to ionize the Hydrogen atom?
E >= 13.6 eV
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• The electronvolt (eV) is a unit of energy • It is the kine7c energy gained by an electron when it
accelerates through an electric poten7al difference of 1 volt
• Since V = W/q, or W = qV, for a single electron
1 eV = 1.602×10−19 C x 1 V ( or 1 J/C) = 1.602×10−19 J
1 eV = 1.60 × 10−19 J
Electronvolts & Joules
58
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the energy of photons for the transi7ons form n = 4 to n = 2 in joules
Energy of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the energy of photons for the transi7ons form n = 4 to n = 2 in joules
n = 4 —> n = 2 -‐0.85 eV – (-‐3.40 eV) = 2.55 eV = 2.55 eV x 1.6 x 10 -‐19 J/eV = 4.08 x 10 -‐19 J
Energy of Photons
SCIENCE – PHYSICSSTEM GARAGE
• How much energy (in joules) is required to ionize the Hydrogen atom?
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• How much energy (in joules) is required to ionize the Hydrogen atom?
E > 13.6 eV
E > 13.6 eV x 1.6 x 10 -‐19 J/eV
E > 2.18 x 10 -‐18 J
Quan7zed Energy Levels
SCIENCE – PHYSICSSTEM GARAGE
• Hydrogen emits only photons of par7cular energies
• The emiBed photon has an energy
E photon = E ini1al – E final
Electron Transi7on
SCIENCE – PHYSICSSTEM GARAGE
Atomic Spectrum
• Hydrogen emits only photons of a set of par7cular energy
• Photon energy E = hf = hc/λ (h = 6.63 × 10–34 J•s) • It emits a set of par7cular wavelengths, and frequencies
SCIENCE – PHYSICSSTEM GARAGE
Atomic Spectrum
Photon is emiBed when electron drops from one quantum state to another
Zero energy
n=1
n=2
n=3 n=4
€
E1 = −13.612 eV
€
E2 = −13.622 eV
€
E3 = −13.632 eV
n=1
n=2
n=3 n=4
€
E1 = −13.612 eV
€
E2 = −13.622 eV
€
E3 = −13.632 eV
Absorbing a photon of correct energy makes electron jump to higher quantum state.
Photon absorbed hf=E2-‐E1
Photon emiBed hf=E2-‐E1
SCIENCE – PHYSICSSTEM GARAGE
• E photon = E ini1al – E final • E photon = h f = h c / λ • The emiBed photon has a
frequency and wavelength:
f = E photon / h
λ = h c / E photon
h = 6.63 × 10–34 J•s (Plank’s constant)
Electron Transi7on
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the frequency of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
Frequency of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the frequency of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
E photon = E ini1al – E final = -‐0.85 eV – (-‐3.40 eV) = 2.55 eV = 2.55 eV x 1.6 x 10 -‐19 J/eV = 4.08 x 10 -‐19 J
f = E / h = 4.08 x 10 -‐19 J / 6.63 × 10–34 J•s = 6.15 x 10 14 Hz
Frequency of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the wavelength of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
Wavelength of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Calculate the wavelength of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
E photon = E ini1al – E final = 4.08 x 10 -‐19 J
λ = h c / E photon = (6.63 × 10 –34 J•s) (3.00 x 10 8 m/s) / 4.08 x 10 -‐19 J = 4.88 x 10 –7 m
Wavelength of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Iden7fy the type of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
Type of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Iden7fy the type of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
E photon = E ini1al – E final = 4.08 x 10 -‐19 J f = E / h = 6.15 x 10 14 Hz
Type of Photons
SCIENCE – PHYSICSSTEM GARAGE
• Electromagne7c spectrum diagram on page 2 of your reference table
Electromagne7c Spectrum
SCIENCE – PHYSICSSTEM GARAGE
• Iden7fy the type of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom
E photon = E ini1al – E final = 4.08 x 10 -‐19 J f = E / h = 6.15 x 10-‐14 Hz
According to the electromagne1c spectrum, it’s visible light (blue)
Type of Photons
SCIENCE – PHYSICSSTEM GARAGE
Atomic Energy Levels & Photon Energy
• What are the resources available in the reference table?
• How to calculate the energy of photon emiBed by an electron changing its energy level?
• How to convert eV to Joule?
• How to calculate the frequency of an emiBed photon?
• How to calculate the wavelength of an emiBed photon?
• How to iden7fy the type of a photon?
SCIENCE – PHYSICSSTEM GARAGE
• Extract the informa7on of Energy Level Diagrams on your reference table
• Calculate the energy of photon by E photon = E ini1al – E final
• Convert the photon energy from eV to Joule by 1 eV = 1.60 × 10−19 J
• Calculate the photon frequency by f = E photon / h • Calculate the photon wavelength by λ = h c / E photon
• Iden7fy the type of a photon according to the electromagne1c spectrum on your reference table
Steps of Solving Energy Level Problems
SCIENCE – PHYSICSSTEM GARAGE
Quantum Physics
SCIENCE – PHYSICSSTEM GARAGE
Quantum Physics • Newtonian laws that work so well for the macroworld of our
daily life do not apply to events in the microworld of atom
• Classic mechanics is for macroworld as quantum mechanics is for the microworld
• Measurements in the macroworld is based on certainty while the measurements in the microworld is governed by probability
SCIENCE – PHYSICSSTEM GARAGE
Heisenberg Uncertainty Principle • Using – Δx = posi7on uncertainty – Δp = momentum uncertainty
• Heisenberg showed that the product ( Δx ) • ( Δp ) is always greater than ( h / 4π )
Planck’s constant
€
Δx( ) Δp( ) ~ /2
SCIENCE – PHYSICSSTEM GARAGE
The End