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Modern Physics

- Light as a Particle

Quantum Physics

- Physics on a very small scale is quantized.
- Quantized phenomena are discontinuous and

discrete. - Atoms can absorb and emit energy, but the energy

intervals are very tiny, and not all energy

levels are allowed for a given atom.

Quantum physics centers on light

Visible spectrum

Electromagnetic spectrum

Light is a ray

- We know from geometric optics that light behaves

as a ray. - This means it travels in a straight line.
- When we study ray optics, we ignore the nature of

light, and focus on how it behaves when it hits a

boundary and reflects or refracts at that

boundary.

But light is also a wave!

- We will study the wave nature of light in more

depth later in the year. - In quantum optics, we use one equation from wave

optics. - c lf
- c 3 x 108m/s (the speed of light in a vacuum)
- l wavelength (m) (distance from crest to crest)
- f frequency (Hz or s-1)

And light behaves as a particle!

- Light has a dual nature.
- In addition to behaving as a wave, it also

behaves like a particle. - It has energy and momentum, just like particles

do. - Particle behavior is pronounced on a very small

level. - A particle of light is called a photon.

Calculating photon energy

- The energy of a photon is calculated from it the

frequency of the light. - E hf
- E energy (J or eV)
- h Plancks constant
- 6.625?10-34 J s
- 4.14 ?10-15 eV s
- f frequency of light (s-1, Hz)

Conceptual checkpoint

- Which has more energy in its photons, a very

bright, powerful red laser or a small key-ring

red laser? - Neither! They both have the same energy per

photon. The big one has more power. - Which has more energy in its photons, a red laser

or a green laser? - The green one has shorter wavelength and higher

frequency. It has more energy per photon.

The electron-volt (eV)

- The electron-volt is the most useful unit on the

atomic level. - If a moving electron is stopped by 1 V of

electric potential, we say it has 1 electron-volt

(or 1 eV) of kinetic energy. - 1 eV 1.602?10-19 J

Sample Problem (similar to 30.10)

- What is the frequency and wavelength of a photon

whose energy is 4.0 x 10-19J?

Solution

- E hf
- 4.0 x 10-19 J (6.625 x 10-34 J s) f
- f 6.04 x 1014 /s (or s-1 or Hz)
- c lf
- 3.00 x 108 m/s l(6.04 x 1014/s)
- l 4.97 x 10-7m 497 nm

Sample Problem

- The bonding energy of H2 is 104.2 kcal/mol.

Determine the frequency and wavelength of a

photon that could split one atom of H2 into two

separate atoms. (1 kcal 4186 J).

Solution

- Convert energy from kcal/mole to joules/molecule
- E (104.2)(4186)/6.02x1023) J/molecule
- E 7.2455 x 10-19 J
- Now find frequency and wavelength as in previous

problem - E hf
- 7.2455 x 10-19 J (6.625 x 10-34 J s) f
- f 1.09 x 1015 /s (or s-1 or Hz)
- c lf
- 3.00 x 108 m/s l(1.09 x 1015 )
- l 2.74 x 10-7m 274 nm

Sample Problem

- How many photons are emitted per second by a

He-Ne laser that emits 3.0 mW of power at a

wavelength of 632.8 nm?

Solution

- Find total energy in one second from power
- P W/t Etot/t
- Etot P t 3.0 x 10-3 J
- Now see how many photons, n, will produce this

energy - E hf (one photon)
- Etot n hf (for n photons)
- E n hc/l (since wavelength is given and not

frequency) - 3.0 x 10-3
- n (6.625 x 10-34 J s) (3.0 x 108 m/s) /

632.8 x 10-9 m - n 9.55 x 1015

Quantized atomic energy levels

- This graph shows allowed quantized energy levels

in a hypothetical atom. - More stable states are those in which the atom

has lower energy. - The more negative the state, the more stable the

atom.

Quantized atomic energy levels

- The highest allowed energy is 0.0 eV. Above this

level, the atom loses its electron. This level is

called the ionization or dissociation level. - The lowest allowed energy is called the ground

state. This is where the atom is most stable. - States between the highest and lowest state are

called excited states.

Quantized atomic energy levels

- Transitions of the electron within the atom must

occur from one allowed energy level to another. - The atom CANNOT EXIST between energy levels.

Absorption of photon by atom

- When a photon of light is absorbed by an atom, it

causes an increase in the energy of the atom. - The photon disappears.
- The energy of the atom increases by exactly the

amount of energy contained in the photon. - The photon can be absorbed ONLY if it can produce

an allowed energy increase in the atom.

Absorption of photon by atom

- When a photon is absorbed, it excites the atom to

higher quantum energy state. - The increase in energy of the atom is given by DE

hf.

Ground state

Absorption Spectrum

- When an atom absorbs photons, it removes the

photons from the white light striking the atom,

resulting in dark bands in the spectrum. - Therefore, a spectrum with dark bands in it is

called an absorption spectrum.

Absorption Spectrum

- Absorption spectra always involve atoms going up

in energy level.

Emission of photon by atom

- When a photon of light is emitted by an atom, it

causes a decrease in the energy of the atom. - A photon of light is created.
- The energy of the atom decreases by exactly the

amount of energy contained in the photon that is

emitted. - The photon can be emitted ONLY if it can produce

an allowed energy decrease in an excited atom.

Emission of photon by atom

- When a photon is emitted from an atom, the atom

drops to lower quantum energy state. - The drop in energy can be computed by DE hf.

Excited state

Emission Spectrum

- When an atom emits photons, it glows! The photons

cause bright lines of light in a spectrum. - Therefore, a spectrum with bright bands in it is

called an emission spectrum.

Emission of photon by atom

- Emission spectra always involve atoms going down

in energy level.

Sample Problem

- What is the frequency and wavelength of the light

that will cause the atom shown to transition from

the ground state to the first excited state? - Draw the transition.

Solution

- DE Ef - Ei
- -5.5 eV (-11.5 eV)
- 6.0 eV
- DE Ephoton hf
- f Ephoton /h
- 6.0 eV / 4.14x10-15 eV s
- 1.45 x 1015 Hz
- c fl
- l c/f
- 3.00 x 108 /1.45 x 1015
- 2.1 x 10-7 m 210 nm

Sample Problem

- What is the longest wavelength of light that when

absorbed will cause the atom shown to ionize from

the ground state? - Draw the transition.

Solution

- DE Ef - Ei
- 0 eV (-11.5 eV)
- 11.5 eV
- DE Ephoton hf hc/l
- l hc/ Ephoton
- (4.14 x 10-15)(3.00 x 108) /11.5
- 1.08 x 10-7 m 108 nm

Sample Problem

- The atom shown is in the second excited state.

What frequencies of light are seen in its

emission spectrum? - Draw the transitions.

Solution

- From second to ground
- Ephoton 8.5 eV
- f E/h
- 8.5 eV / 4.14x10-15 eV s
- 2.05 x 1015 Hz
- From second to first
- E 2.5 eV
- f E/h 6.04 x 1014 Hz
- From first to ground
- E 6.0 eV
- f E/h 1.45 x 1015 Hz

Remember atoms can absorb photons

- Weve seen that if you shine light on atoms, they

can absorb photons and increase in energy. - The transition shown is the absorption of an 8.0

eV photon by this atom. - You can use Plancks equation to calculate the

frequency and wavelength of this photon.

Ionization level

0.0 eV

-4.0 eV

Ground state (lowest energy level)

-12.0 eV

Photoelectric Effect

- Some photoactive metals can absorb photons that

not only ionize the metal, but give the electron

enough kinetic energy to escape from the atom and

travel away from it. - The electrons that escape are often called

photoelectrons.

e-

Ionization level

0.0 eV

-8.0 eV

- The binding energy or work function is the

energy necessary to promote the electron to the

ionization level. - The kinetic energy of the electron is the extra

energy provided by the photon.

Ground state (lowest energy level)

-12.0 eV

Photoelectric Effect

- Photon Energy
- Work Function
- Kinetic Energy
- hf f Kmax
- Kmax hf f
- Kmax Kinetic energy of photoelectrons
- hf energy of the photon
- f binding energy or work function of the

metal.

e-

Ionization level

0.0 eV

-8.0 eV

Ground state (lowest energy level)

-12.0 eV

Sample problem

- Suppose the maximum wavelength a photon can have

and still eject an electron from a metal is 340

nm. What is the work function of the metal

surface?

Solution

- The longest wavelength is the lowest energy, and

will provide no extra kinetic energy for the

electron. - Kmax hf f
- f hf Kmax hc/l Kmax
- f 4.14E-153E8 / 340E-9 0
- f 3.7 eV

Sample problem

- Zinc and cadmium have photoelectric work

functions given by WZn 4.33 eV and WCd 4.22

eV. - A) If illuminated with light of the same

frequency, which one gives photoelectrons with

the most kinetic energy? - B) Calculate the maximum kinetic energy of

photoelectrons from each surface for 275 nm light.

Solution

- A) Since Cd has the smaller work function, its

photoelectrons have more energy given Kmax hf

f. - B) Kmax hf f and f c/l
- Kmax hc/l - f
- for Cd
- Kmax 4.14E-153E8 / 275E-9 4.22 eV
- Kmax 0.30 eV for Zn
- Kmax 4.14E-153E8 / 275E-9 4.33 eV
- Kmax 0.19 eV

Review of Photoelectric Effect

- Kmax hf f
- Kmax Kinetic energy of photoelectrons
- hf energy of the photon
- f binding energy or work function of the

metal.

Ionization level

0.0 eV

-8.0 eV

Ground state (lowest energy level)

-12.0 eV

Question

- The photoelectric equation is Kmax hf f.

Suppose you graph f on horizontal axis and Kmax

on vertical. What information do you get from the

slope and intercept? - Slope Plancks Constant
- Intercept -?

The Photoelectric Effect experiment

- The Photoelectric Effect experiment is one of the

most famous experiments in modern physics. - The experiment is based on measuring the

frequencies of light shining on a metal, and

measuring the energy of the photoelectrons

produced by seeing how much voltage is needed to

stop them. - Albert Einstein won the Nobel Prize by explaining

the results.

Photoelectric Effect experiment

At voltages less negative than Vs, the

photoelectrons have enough kinetic energy to

reach the collector.

If the potential is Vs, or more negative than Vs,

the electrons dont have enough energy to reach

the collector, and the current stops.

Collector (-)

metal ()

e-

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e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

V

e-

e-

e-

A

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Experimental determination of the Kinetic Energy

of a photoelectron

- The kinetic energy of photoelectrons can be

determined from the voltage (stopping potential)

necessary to stop the electron. - If it takes 6.5 Volts to stop the electron, it

has 6.5 eV of kinetic energy.

Strange results in the Photoelectric Effect

experiment

- Voltage necessary to stop electrons is

independent of intensity (brightness) of light.

It depends only on the lights frequency (or

color). - Photoelectrons are not released below a certain

frequency, regardless of intensity of light. - The release of photoelectrons is instantaneous,

even in very feeble light, provided the frequency

is above the cutoff.

Voltage versus current for different intensities

of light.

Number of electrons (current) increases with

brightness, but energy of electrons doesnt!

I

V

Vs, the voltage needed to stop the electrons,

doesnt change with light intensity. That means

the kinetic energy of the electrons is

independent of how bright the light is.

Stopping Potential

Voltage versus current for different frequencies

of light.

Energy of electrons increases as the energy of

the light increases.

f3 gt f2 gt f1

I

V

Vs changes with light frequency. That means the

kinetic energy of the photoelectrons is dependent

on light color.

Stopping Potential

Graph of Photoelectric Equation

Kmax

Kmax h f - f y m x b

f

Photoelectric simulations

- Link for simulated photoelectric effect

experiment - http//lectureonline.cl.msu.edu/mmp/kap28/PhotoEf

fect/photo.htm

Assignment (due Friday next week)

- Run the photoelectric experiment for all three

metals. You must collect at least 5 data points

for each metal. - Graph the data such that Plancks constant can be

determined from the slope and the work function

of the metal can be determined from the

y-intercept. - Your report consists of three data tables and

three graphs, one for each metal. Clearly

indicate the results you got for each metal. - Graphs and tables may be done by hand on graph

paper, or you may use Excel or another

spreadsheet program if you like.

Wave-Particle Duality

- Waves act like particles sometimes and particles

act like waves sometimes. - This is most easily observed for very energetic

photons (gamma or x-Ray) or very tiny particles

(elections or nucleons)

Particles and Photons both have Energy

- A moving particle has kinetic energy
- E K ½ mv2
- A particle has most of its energy locked up in

its mass. - E mc2
- A photons energy is calculated using its

frequency - E hf

Particles and Photons both have Momentum

- For a particle that is moving
- p mv
- For a photon
- p h/?
- Check out the units! They are those of momentum.s

Particles and Photons both have a Wavelength

- For a photon
- ? c/f
- For a particle
- ? h/p where p mv
- This is referred to as the deBroglie wavelength

We have experimental proof of Wave-Particle

Duality

- Compton scattering
- Proof that photons have momentum.
- High-energy photons collided with electrons

exhibit conservation of momentum. - Davisson-Germer Experiement
- Verified that electrons have wave properties by

proving that they diffract. - Electrons were shone on a metal surface and

acted like light by diffraction and interference.

Sample problem

- What is the momentum of photons that have a

wavelength of 620 nm?

Sample problem

- What is the wavelength of a 2,200 kg elephant

running at 1.2 m/s?