day 1 modern physics note: each topic is sectioned into “days” numbered from 1 to 7. this would...

Day 1

Modern PhysicsNOTE: each topic is sectioned into “days” numbered from 1 to 7. This would be a

good pace to follow as you make your way through the unit. If you learn one section

per day, you will be done in one week!

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 just 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 = f– c: 3 x 108 m/s (the speed of light in a

vacuum)– : 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. This particle behavior shows up under certain circumstances.

• A particle of light is called a “photon”.

Calculating photon energy

• The energy of a photon is calculated from the frequency of the light.

• E = hf– E: energy (J or eV)– h: Planck’s constant

• 6.62510-34 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 = 1.60210-19 J

Sample Problem• What is the frequency and

wavelength of a photon whose energy is 4.0 x 10-19J?

Sample Problem • The bonding energy of H2 is 104.2 kcal/mol. Determine the frequency and wavelength of a photon that could split one molecule of H2 into two separate atoms. (1 kcal = 4186 J).

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?

Day 2

Atomic Energy Levels

AA differeNNt look ATAT an OOld coMMpanion Line Spectra vs. Continuous Spectra

– Line Spectrum - contains only certain colors• Only certain lines of color appear in the

spectrum

– Continuous Spectrum - contains all the colors• A continuous band of colors appears in

the spectrum

The Crayon Perspective

Spectroscope activity Look at an incandescent bulb

(Continuous spectrum) Look at a fluorescent bulb (Line

spectrum, nearly continuous)

The Bohr Model First there was Rutherford.

– Nuclear Model of the atom: electrons have energy and orbit the nucleus.

Then there was Planck.– Energy is Quantized (stairs), not continuous

(a ramp): there must be energy levels(or “steps”) for the electrons to orbit at.

– It may help to equate the word “quantum” with “level”.

The Bohr Model: Anything but ‘Bohring’

Niels Bohr thought, “the energy of the electrons orbiting a nucleus must be quantized.”

So he came up with different energy levels (”quantums”) for the electrons.– He gave the energy levels (quantums)

numbers. These are what we call “Quantum numbers”. They are abbreviated with an “n” and the level number. (For example: n1 is the first energy level)

The Bohr Model: Anything but ‘Bohring’ The lowest energy level (n1) is called

the ground state. When an electron absorbs a photon of

high enough energy (or, high enough frequency), that electron jumps to the next energy level.

Any energy level where an electron is higher than the ground state is called an excited state.

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.

0.0 eV

-1.0 eV

-3.0 eV

-5.5 eV

-11.5 eV

Ionization level

Ground state (lowest energy level)

First excited state

Second excited state

Third excited state

more

sta

ble

less

sta

ble


• 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.

0.0 eV

-1.0 eV

-3.0 eV

-5.5 eV

-11.5 eV

Ionization level


First excited state


Third excited state


• Transitions of the electron within the atom must occur from one allowed energy level to another.

• The atom CANNOT EXIST between energy levels.

0.0 eV

-1.0 eV

-3.0 eV

-5.5 eV

-11.5 eV

Ionization level


First excited state


Third excited state

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 E = hf.

0 eV

-10 eV

Ground state

E

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.

0 eV

-10 eV

ionized

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.


• When a photon is emitted from an atom, the atom drops to lower quantum energy state.

• The drop in energy can be computed by E = hf.

0 eV

-10 eV

Excited state

E

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 spectra always involve atoms going down in energy level.

0 eV

-10 eV

ionized

Sample ProblemA. 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?

B. Draw the transition.0.0 eV

-1.0 eV

-3.0 eV

-5.5 eV

-11.5 eV

Ionization level


First excited state


Third excited state

Sample ProblemA. What is the longest wavelength of light that when absorbed will cause the atom shown to ionize from the ground state?

B. Draw the transition.0.0 eV

-1.0 eV

-3.0 eV

-5.5 eV

-11.5 eV

Ionization level


First excited state


Third excited state

Sample ProblemA. The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum?

B. Draw the transitions.

0.0 eV

-1.0 eV

-3.0 eV

-5.5 eV

-11.5 eV

Ionization level


First excited state


Third excited state

Day 3

Photoelectric effect

Review Slide: Remember atoms can absorb photons

• We’ve 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 Planck’s equation to calculate the frequency and wavelength of this photon.

0.0 eV

-12.0 eV

Ionization level


-4.0 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”.

• 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.

0.0 eV

-12.0 eV

Ionization level


-8.0 eV

Work function

Kinetic energy

Ph

oto

n e

nerg

y

e-

Photoelectric Effect

• Photon Energy = Work Function + Kinetic Energy• hf = + Kmax

• Kmax = hf – – Kmax: Kinetic energy of

“photoelectrons”– hf: energy of the

photon– : binding energy or

“work function” of the metal.

0.0 eV

-12.0 eV

Ionization level


-8.0 eV

Work Function

Kinetic energy

Ph

oto

n e

nerg

y

e-

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?

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.

Question

The photoelectric equation is Kmax = hf – . Suppose you graph f on horizontal axis and Kmax on vertical. What information do you get from the slope and intercept?

Slope: Planck’s ConstantIntercept: -

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

metal(+)

A

V

Collector (-)

e- e- e- e- e- e-

e-

e-

e-

e-e-e-e-e-e-

e-

e-

light

e- e- e- e-e- e- e- e- e-

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 don’t have enough energy to reach the collector, and the current stops. light

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 light’s 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.

V

I

Vs

I1

I2

I3

Vs, the voltage needed to stop the electrons, doesn’t change with light intensity.That means the kinetic energy of the electrons is independent of how bright the light is.

“StoppingPotential”

Number of electrons (current) increases with brightness, but energy of electrons doesn’t!

Voltage versus current for different frequencies of light.

V

I

Vs,1

f1f2

Vs,2

f3

Vs,3

f3 > f2 > f1

Vs changes with light frequency.That means the kinetic energy of the photoelectrons is dependent on light color.

“StoppingPotential”

Energy of electrons increases as the energy of the light increases.

Day 4

Photoelectric effect simulation laboratory

Graph of Photoelectric Equation

f

Kmax

Kmax = h f - y = m x + b

slope = h(Planck’s Constant)

(binding energy)

Cut-off frequency

Photoelectric simulations

• Link for simulated photoelectric effect experiment– http://lectureonline.cl.msu.edu/~mmp

/kap28/PhotoEffect/photo.htm

Lab Assignment

• Run the photoelectric experiment for both metals. You must collect at least 5 data points for each metal.

• Graph the data such that Planck’s constant can be determined from the slope, and the work function can be determined from the y-intercept.

• Your report will consist of two data tables and two graphs, one for each metal, preferably done in Excel. You must do a proper curve fit for your data, and clearly indicate Planck’s constant, the work function, and the cut-off frequency for each metal.

• Reports are due the week we return from break. They may be emailed to me, or printed and brought to class.

Day 5

Nuclear Decay

A typical nucleus

C12

6

Element name

Atomic mass: protons plus neutrons

Atomic number: protons

Isotopes

• Isotopes have the same atomic number and different atomic mass.

• Isotopes have similar or identical chemistry.

• Isotopes have different nuclear behavior.

• Examples:

Uranium isotopes

U238

92U

235

92

Nucleons

• Nucleons are particles that exist in the nucleus of an atom.

• Proton•Charge: +e•Mass: 1 amu

• Neutron•Charge: 0•Mass: 1 amu

p11

n10

Nuclear reactions

• Nuclear Decay: a spontaneous process in which an unstable nucleus ejects a particle and changes to another nucleus.– Alpha decay– Beta decay

• Beta Minus• Positron

• Fission: a nucleus splits into two fragments of roughly equal size.

• Fusion: Two nuclei combine to form another nucleus.

Decay Reactions

• Alpha decay– A nucleus ejects an alpha particle, which

is just a helium nucleus.• Beta decay

– A nucleus ejects a negative electron.• Positron decay

– A nucleus ejects a positive electron.• Simulations

– http://library.thinkquest.org/17940/texts/radioactivity/radioactivity.html

Alpha Decay

Alpha particle (helium nucleus) is released. Alpha decay only occurs with very heavy elements.

239 235 494 92 2Pu U He

Beta (-) Decay

A beta particle (negative electron) is released. Beta decay occurs when a nucleus has too many neutrons for the protons present. A neutron converts to a proton. An antineutrino is also released.

14 14 06 7 1C N e

Positron (+) Decay

Positron (positive electron) is released. Positron decay occurs when a nucleus has too many protons for the neutrons present. A proton converts to a neutron. A neutrino is also released.

2 2 02 1 1He H e

Neutrino and Anti-Neutrino

• Proposed to make beta and positron decay obey conservation of energy.

• These particles possess energy and spin, but do not possess mass or charge.

• They do not react easily with matter, and are extremely hard to detect.

Gamma Radiation, • Gamma radiation is

electromagnetic in nature.

• Gamma photons are released by atoms which have just undergone a nuclear reaction when the excited new nucleus drops to its ground state.

• The high energy in a gamma photon is calculated by E = hf.

Calculation of energy released in nuclear

reactionss

1. Add up the mass (in atomic mass units, u) of the reactants. You can find the mass in Appendix E of your textbook.

2. Add up the mass (in atomic mass units, u) of the products.

3. Find the difference between reactant and product mass. The missing mass has been converted to energy.

4. Convert mass to kg ( 1 u = 1.66 x 10-27 kg)5. Use E = mc2 to calculate energy released.

Sample ProblemComplete the reaction, identify the type of decay, and calculate the energy.

232 22890 88 ?Th Ra

Sample ProblemComplete the reaction, identify the type of decay, and calculate the energy.

234 091 1? ?Pa e

Day 6

Nuclear Fusion and Fission

Fission

• Fission occurs when an unstable heavy nucleus splits apart into two lighter nuclei, forming two new elements.

• Fission can be induced by free neutrons.• Mass is destroyed and energy produced according to E

= mc2.• http://library.thinkquest.org/17940/texts/fission/fission.h

tml• http://www.atomicarchive.com/Movies/index.shtml

Neutron-induced fission

• Neutron-induced fission produces a “chain reaction.” What does that mean?

• Nuclear power plants operate by harnessing the energy released in fission in by controlling the chain reaction.

• Nuclear weapons depend upon the initiation of an uncontrolled fission reaction.

Critical Mass

• The neutrons released from an atom that has undergone fission cannot immediately be absorbed by other nearby fissionable nuclei until they slow down to “thermal” levels.

• How can this concept be used to explain why a chain reaction in nuclear fission will not occur unless a “critical mass” of the fissionable element is present at the same location?

Nuclear Reactors

• Nuclear reactors produce electrical energy through fission.• Advantages are that a large amount of energy is produced

without burning fossil fuels or creating greenhouse gases.• A disadvantage is the production of highly radioactive waste.• Another simulation appears at

– http://www.howstuffworks.com/nuclear-power.htm

University of Wisconsin Nuclear Reactor Tour

Nuclear Weapons

• Nuclear weapons have been used only twice, although they have been tested thousands of times.

• Weapons based on nuclear fission involve slamming together enough material to produce an uncontrolled fission chain reaction.

Nagasaki, Japan

Little Boy was dropped on Hiroshima and contained U-235 produced in Oak Ridge, TN.

Fission

• Fission occurs only with very heavy elements, since fissionable nuclei are too large to be stable.

• A charge/mass calculation is performed to balance the nuclear equation.

• Mass is destroyed and energy produced according to E = mc2.

1 239 133 100 10 94 51 43 06n Pu Sb Tc n

Sample problem• Complete the following

reaction and determine the energy released.

1 235 90 10 92 38 0? 5n U Sr n

Fusion

• Fusion occurs when two light nuclei come together to form a new nucleus of a new element.

• Fusion is the most energetic of all nuclear reactions.• Energy is produced by fusion in the sun.• Fusion of light elements can result in non-

radioactive waste.

He 2 2

H1

1 H1

1

Fusion

• Fusion is the reaction that powers the sun, but it has not been reliably sustained on earth in a controlled reaction.

• Advantages to developing controlled fusion would be the tremendous energy output and the lack of radioactive waste products.

• Disadvantages are – we don’t know if we’ll be technical able to do it on earth!

Sample Problem

• You fuse a free proton with a free neutron to form a deuterium nucleus. How much energy is released?

Mass defect

• This strange term is used to indicate how much mass is destroyed when a nucleus is created from its component parts.

• The mass defect is generally much, much less than the mass of a proton or neutron, but is significant nonetheless.

• The loss of mass results in creation of energy, according to E = mc2.

Sample problem• What is the mass defect

of 12C in atomic mass units? How does this relate to mass in kg and energy in eV and J?

Day 7

Wave-Particle Duality

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

• We know from mechanics that a moving particle has kinetic energy– E = K = ½ mv2

• However, a particle really has most of its energy locked up in its mass. – E = mc2

• A photon’s energy is calculated using its frequency– E = hf

Particles and Photons both have Momentum

• We know from mechanics that a particle that is moving has momentum– p = mv

• For a photon– p = h/– Check out the units! They are those of

momentum.

What’s the matter with Matter?

Light travels in waves, but also bounces off of things like particles would.

“What if matter behaves the same way as light does?” - Louis de Broglie

Well wha’ do ya know, it DOES! Matter is thought of as different sized

particles. The wavelike behavior of these particles is aptly named matter waves.

Wavy Matter A particle’s mass has a lot to do with the

wavelength it travels at. If a particle has the mass of a baseball,

the wavelength will be so small that it cannot be observed.

BUTBUT if the particle has a very small mass, like that of an electronelectron for example, then the wavelength is large enough to equal the wavelengths of light, and scientists can observe that.

Particles and Photons both have a Wavelength

• A photon of light has a wavelength, since light is also a wave– = c/f

• Hard as it may be to believe, particles also have wavelengths = h/p where p = mv– This is referred to as the deBroglie

wavelength and is pronounced for very tiny particles.

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?

Changes made in 2002• Removed (5% of syllabus)• Alpha particle scattering• Rutherford scattering• Bohr model (but energy levels remain)• Radioactivity• Half life• Unchanged• Wave particle dynamics• Nuclear reactions• Mass energy equivalence

day 1 modern physics note: each topic is sectioned into “days” numbered from 1 to 7. this would...

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