The Description of the microscopic world

Previous Lecture: Quantization of light, photonsPhotoelectric effectParticle-Wave dualism

This Lecture: Matter wavesUncertainty Principle Wave functionsStart the atom

MTE3 on Wed 23, 5:30-7:00 pm, Ch 2103 and SH 180, same sessions in each room

Alternate Exams on Wed2:30-4:00 pm6:00-7:30 pmin the Lab room

Send your requests for Alternate Examsby email specifying the class conflict

MTE 3 Contents

Amperes Law and force between wires with current (32.6, 32.8) Faradays Law and Induction (ch 33, no inductance 33.8-10) Maxwell equations, EM waves and Polarization (ch 34, no 34.2) Photoelectric effect (38.1-2-3) Matter waves and De Broglie wavelength (38.4) Atom (37.6, 37.8-9, 38.5-7) Wave function and Uncertainty (39)

3

Quantization of light

Light is made of quanta of energy called photons

quantum of energy: E=hf f = frequency of light

Photon is a particle, but moves at speed of light!

This is possible because it has zero mass.

Zero mass, but it does have momentum:

Photon momentum p=E/c (remember U/c for radiation)

Photoelectric effect (1905)

No matter how intense is the light: until the light wavelength passes a certain threshold, no electrons are ejected.

Kmax = h

How much is a quantum of green light?

One quantum of energy for 500 nm light (green)

E = hf = hc

=6.634 1034 Js( ) 3108m /s( )

500 109m= 4 1019J

We need a convenient unit for such a small energy!

1 electron-volt = 1 eV = |charge on electron|x (1 volt) = 1.602x10-19 J

Energy of an electron accelerated in a potential difference of 1 V

In these units,

E(1 green photon) = (4x10-19 J)x(1 eV / 1.602x10-19 J) = 2.5 eV

hc =1240 eV nm so you can use 1240 eV nm/500nm = 2.5 eV

Quiz on photoelectric effectWhich of the following is not true of photoelectric emission?A. increasing the light intensity causes no change in the kinetic energy of photoelectronsB. the max energy of photoelectrons depends on the frequency of light illuminating the metalC. increasing the intensity of the light will increase the KE of photoelectronsD. Doubling the light intensity doubles the number of photoelectrons emitted

6

A. is true because the intensity is connected to the number of electrons not to the energy of each onesB. is true because Kmax fC. is false because Kmax depends on fD. Intensity = Power/Area = energy/(time x A) = (Nhf/time x Area)

Is Light a Wave or a Particle?

Wave Electric and Magnetic fields act like waves Superposition, Interference and Diffraction

Particle Photons Photo-electric effect Compton Effect

Sometimes Particle Sometimes Wavedepending on the experiment!

Wave properties of particles

1924 graduate student Nobel Prize in 1929

de Broglie wavelength

De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,...

Should be able to see interference and diffraction for any material particle!!

Wavelength of an electron of 1 eV

de Broglie wavelength

Result: = 1.23 nm

Solve forIf m of particle is large small and wave properties not noticeable

me = 9.1 x 10-31 = 0.511 MeV/c2

De Broglie question

10

Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each have 10 Joules of kinetic energy.

A) bowling > golfB) bowling = golfC) bowling < golf

The largest the mass of the object the less noticeable are

the quantistic effects!Football launched by Brett Favre can go at 30m/s and m = 0.4kg

=hp

=6.6 1034 Js0.4kg 30m /s

= 5.5 1035m

Light properties as a wave

Light has wavelength, frequency, speed f = speed

Light shows interference and diffraction phenomena

Is an Electron a Particle or a Wave? Particle: you can bounce things off them. How would know if electron was a wave?

Look for interference!

This is what we observe like if 1 electron passes through both slits!!

We destroy interference illuminatingto determine the slit they go through

Electron Diffraction: the experiment Parallel beams of mono-energetic electrons on a double slit slit widths

Davisson-Germer experiment

Diffraction of electrons from a nickel single crystal.

Found pattern by heating just by chance. Nichel formed a crystalline structure.

Established that electrons are waves.

54 eV electrons (=0.17nm)

Bright spot: constructive interference

Davisson: Nobel Prize 1937

15

Whats your view of atoms?

16

Hystory of Atoms

Thompsons classical model - raisin-cake (1897): cloud of + charge with embedded e-

Problem: charges cannot be in equilibrium

Planetary model Positive charge concentrated in the nucleus ( 10-15 m) Electrons orbit the nucleus (r~10-10 m)

Problem1: emission and absorption at specific frequenciesProblem2: electrons on circular orbits radiate

17

Rutherfords experiment (1911)

Most of the alpha-particles (ionized He nuclei made of 2p+2n) not deflected much but a few bounced back

18

Bohrs Model of Hydrogen Atom (1913)Postulate 1: Electron moves in circular orbits where it does not radiate (stationary states)

Postulate 2: radiation emitted in transitions between stationary states

Orbit radius: rn = n2 a0

orbital angular momentum quantized L = mvr = n h/2

Ei E f = hf

Notice: Sometimes fis indicated by

Ef

Ei

Emitted photon has energy hf

a0 = 0.053 nm

En = -13.6 eV/n2

19

Emitting and absorbing lightZero energy

n=1

n=2

n=3n=4

E1 = 13.612

eV

E2 = 13.622

eV

E3 = 13.6

32 eV

n=1

n=2

n=3n=4

E1 = 13.612

eV

E2 = 13.622

eV

E3 = 13.6

32 eV

Photon absorbed hf=E2-E1

Photon emittedhf=E2-E1

Ener

gy

axis

20

Question

This quantum system has equally-spaced energy levels as shown. Which photon could possibly be absorbed by this system?

E1=1 eV

E2=3 eV

E3=5 eV

E3=7 eV

Ephoton =hc

=1240 eV nm

A. 1240 nm

B. 413 nm

C. 310 nm

D. 248 nm

2eV 1240 /4132eV 1240 /3102eV 1240 /2484eV 1240 /12404eV 1240 /4134eV =1240 /310

21

Why quantized orbits?

Electron is a wave. Its propagation direction is

around circumference of orbit. Wavelength = h / p

Waves on a circular orbit?

Incorporating wave nature of electron gives an intuitive understanding of quantized orbits

22

Standing waves on a string

Fundamental, wavelength 2L/1=2L, frequency f

1st harmonic, wavelength 2L/2=L, frequency 2f

2nd harmonic, wavelength 2L/3,frequency 3f

/2

/2

/2

n =2Ln

Standing wavedisplacement:Boundary conditions:

D(x, t) = 2Asinkxcost

sinkx = 0

sinkL = 0

A guitar vibrates at frequency that depends on string length

freq

uenc

yn=1

n=2

n=3

n=4

Vibrational modes equally spaced in f

. .

.

23

Waves in a circular Donut flute

Blow in here

Wavelength

Integer number of wavelengths around circumference.

Otherwise destructive interference occurs when wave travels around ring and interferes with itself

Wind instrument with particular fingering plays a particular pitch (or wavelength)

24

Quantization from de Broglie

Circumference

deBroglie:

Result:

giving

L=angular momentum = ,quantized!

= 2rn = n

Integer number wavelengths along circumference of radius rn

=hp

=hmev

2rn =nhmev

mevr = nh2

= nh

Bohr H atom question Peter Flanarys sculpture Wave outside Chamberlin What quantum state of H?

25

Integer number of wavelengths around circumference.

L = pr = n h2

h

= n h2r

2r = n

A. n =2B. n = 3C. n = 4

Lets demonstrate E= -13.6Z2 eV /n2

26

F = k Ze2

r2= m v

2

rmvr = nh

k Ze2

r= mv 2

Total energy = kinetic energy + potential energy = kinetic energy + eV

r = k Ze2

mv 2

v = nhmr

Substitute (2) in (1):

(1)

(2)

r = k Ze2m2r2

mn2h2 r = n

2

Zh2

me2k=n2

Z(1.055 1034 )2

9.111031 (1.6 1019)2 9 109=n2

Z0.531010m

r = n2

Za0

E = p2

2m k Ze

2

r=mv 2

2 k Ze

2

r= k Ze

2

2r= k Ze

2

2Zme2kn2h2

= Z 2

n2k 2me4

2h2= 13.6eV Z

2

n2

E = Z2

n2(9 109)2 9.111031 (1.6 1019)4

2 (1.055 1034 )2=

Z 2

n22.2 1018J = Z

2

n213.6eV

a0 = Bohr radius = 0.53 x 10-10 m = 0.53

Z=n. of protons in nucleus of H-like atom