Presentation Lesson 27 Quantum Physicsstemgarage.org/Toolbox_Physics/Physics Presentations/Presentatio… · STEM GARAGE SCIENCE – PHYSICS The$Planetary$Model$of$Atom$ • Niels$Bohr’s$model$

SCIENCE – PHYSICSSTEM GARAGE

Quantum Physics

Chin-‐Sung Lin


The Model of Atom


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


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!


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



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


•  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



•  Hydrogen emits only photons of a par7cular wavelength, frequency

•  Photon energy = hf, so this means a par7cular energy



•  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



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 •  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


Models of Light


The Model of Light •  Two primary models of light: the par7cle model and the

wave model


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


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


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


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



•  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



•  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



•  Light travels as a wave

•  Light interacts with maBer as a stream of par7cles


Waves vs. Par7cles


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


Waves vs. Par7cles •  Which model can explain the phenomenon?


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


Waves vs. Par7cles

Electron beam is directed toward a crystal


Waves vs. Par7cles

Diffrac7on & interference paBern is observed


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!


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


Material Waves


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


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( )


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


Material Waves

•  Example: Calculate the de Broglie wavelength of an electron traveling at 2% the speed of light


Material Waves

•  Example: Calculate the de Broglie wavelength of an ball traveling at 330 m/s


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


Material Waves

•  The electron microscope can dis7nguish detail not possible with op7cal microscopes


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


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


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


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


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


Rela7ve Sizes of Atoms


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


Rela7ve Sizes of Atoms


Atomic Energy Levels & Photon Energy


•  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


•  Energy level diagrams on page 3 of your reference table

Quan7zed Energy Levels


•  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



•  How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 4?



•  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



•  How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 7 ?



•  How many different transi7ons to the lower energy levels can an electron have when the electron is at n = 7 ?

6 different transi1ons



•  Calculate the energy of photons for those possible transi7ons form n = 4

Energy of Photons


•  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


•  How much energy is required to ionize the Hydrogen atom?



•  How much energy is required to ionize the Hydrogen atom?

E >= 13.6 eV



•  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


•  Calculate the energy of photons for the transi7ons form n = 4 to n = 2 in joules

Energy of Photons


•  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


•  How much energy (in joules) is required to ionize the Hydrogen atom?



•  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



•  Hydrogen emits only photons of par7cular energies

•  The emiBed photon has an energy

E photon = E ini1al – E final

Electron Transi7on


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


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


•  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


•  Calculate the frequency of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom

Frequency of Photons


•  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


•  Calculate the wavelength of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom

Wavelength of Photons


•  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


•  Iden7fy the type of photons for the transi7ons form n = 4 to n = 2 in a hydrogen atom

Type of Photons



E photon = E ini1al – E final = 4.08 x 10 -‐19 J f = E / h = 6.15 x 10 14 Hz

Type of Photons


•  Electromagne7c spectrum diagram on page 2 of your reference table

Electromagne7c Spectrum



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


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?


•  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


Quantum Physics


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


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


The End

Documents

Presentation Lesson 27 Quantum Physicsstemgarage.org/Toolbox_Physics/Physics Presentations/Presentatio… · STEM GARAGE SCIENCE – PHYSICS The$Planetary$Model$of$Atom$ • Niels$Bohr’s$model$