The worksheet for the simulation is in the student’s booklets.

Quantum and Nuclear Physics (B) Mr. Klapholz Shaker Heights High School

Summary of the Photoelectric effect: Light makes electrons shoot off of metal (data). This shows that light is a particle (theory). And now a detailed look at the photoelectric effect…

Light In 1660 Newton thought light was a particle. In 1801 Young showed (in the “Double slit experiment”) that light exhibited wave phenomena (interference and diffraction). Also the polarization of light makes only makes sense if light is a wave. So in the first half of the 1800’s, everyone was comfortable that light was a wave. It wasn’t that simple…

The Photoelectric Effect From data trickled in about a particular experiment that would really get people thinking. It would start one of the great “paradigm shifts” in human knowledge.

The Electroscope is a simple charge indicator.

Under the right circumstances, if you shine light on metal, it will become positively charged.

Light can neutralize a negatively charged piece of metal…

but if the low frequency light is sent in, then no electrons are emitted.

The photoelectric effect basic facts: It is a big deal for electrons to be emitted by the metal because the electrons are attracted to the protons in the metal (yet the electrons still leave). Brighter light produces more electrons, but not electrons with more kinetic energy. (!) Greater frequencies yield greater kinetic energy for electrons (as individuals, not as a groups). (!) Below a ‘threshold frequency’ absolutely no electrons are emitted. (!) There is no lag time: electrons are emitted as soon as the light is turned on. (!)

Farewell to the wave theory of light Every one of the (!) symbols on the previous slide made no sense if light was a wave. For example, if light was a wave, then many low- energy light waves would eventually cause an electron to be emitted, but in the lab, low-energy light never makes a photelectron. Also, waves of greater light intensity would have affected the kinetic energy of the electrons, but this never happened.

Einstein !

Einstein won the Nobel prize for his theory on the photoelectric effect (1905). Light is made of particles of light (“photons”). For an electron to be emitted, exactly one photon must be absorbed. The greater the intensity of light, the greater the number of photons (per second), and the greater the number of electrons emitted. It seems so simple now.

Time out for a moment of Duality Light behaves as a wave and as a particle.

Planck had shown how energy and frequency were related: E = hf. High frequency light (like UV) has high energy. Red light has low energy. Violet light, even dim violet light, can make an electron leave the metal, with plenty of kinetic energy to spare. Red light, even bright red light, cannot make even one electron leave the metal. [Of course, the details depend on the type of metal, the temperature, and so on.]

Threshold It takes a particular amount of energy to get an electron to leave the metal, due to Coulomb attraction. In this context, this energy is called the ‘work function’ (  ). If a photon does not have at least the energy of the work function, then there is no way it will make an electron leave the metal.

Our first photoelectric equation: Energy going in = Energy used + Energy coming out hf = Energy used + Energy coming out hf =  + Energy coming out hf =  + KE of electron What would happen if the work function was greater than the energy of the incoming photon?

Millikan’s experiment (notice the polarity) …

A close look at the applied voltage For the moment, assume that the light is of great enough frequency to eject some electrons. The voltage stops the electrons from leaving the target. The smallest voltage that can turn around the electrons is called the “Stopping Potential” (V).

A close look at the applied voltage Not all of the electrons that leave the target have the same value for kinetic energy. Let’s focus on the most energetic electrons, the ones with KE max. Why can’t the electrons that leave the target with KE max get to the detector? … There is an electrical force that turns the electrons around. It takes a lot of energy to still make it to the detector.

A close look at the applied voltage The experimenter (Millikan) used many different frequencies of light (that is his independent variable) and for each one he measured the ‘Stopping Potential’ (the smallest voltage that prevented electrons from leaving the target)…

A close look at the applied voltage Frequency / × HzStopping Potential / V

A close look at the applied voltage electrical energy / charge = voltage electrical energy = charge × voltage energy = qV If V is tuned just right, so that the voltage is as small as possible but still prevents every electron from making it to the detector, then it is removing an amount of energy equal to the maximum kinetic energy of the electrons. eV = KE max.

A close look at the applied voltage hf =  + Kinetic Energy of Electron hf =  + eV Remember that V is the smallest possible voltage that stops the photelectrons.

A close look at the applied voltage hf =  + eV What would you see if you graphed Stopping Voltage vs. frequency ? V = (h/e) f – (  /e) y = mx + b It makes a line, the slope is h/e. The y-intercept (  /e) gives the work function. The threshold frequency is also easy to spot…

Stopping Voltage vs. Frequency

Different metals have different work functions (different y-intercepts) and different threshold frequencies.

A variation of our photoelectric equation: Conservation of energy gave us: Energy in = Energy out hf =  + KE hf =  + eV Every term is an energy.  is the minimum energy required to remove one electron; this corresponds to the threshold frequency (f 0 ) the minimum frequency that will liberate one electron:  = hf 0 …

A variation of our photoelectric equation: hf =  + eV hf = hf 0 + eV Let’s revisit the graph with this equation in mind. hf = hf 0 + eV V = (h/e)f - (h/e)f 0 For what value of f is V = 0? V = 0 when f = f 0. See this on the graph…

Stopping Voltage vs. Frequency

Spotlight on the photon The energy of the photon is E = hf. The speed of a photon in a vacuum is 3 x 10 8 m s -1. The momentum of massive things is p = mv. The mass of the photon is 0, yet experiments show that it has momentum. What is the momentum of a photon? p = E / c.

If you bounce electrons off of a crystal, the result is the same as bouncing a wave off of a crystal (Davisson-Germer experiment).

Matter Waves Matter acts as a wave. The de Broglie wavelength: = h / p = h / mv Which diffracts more, small wavelengths or large wavelengths? sin  = / b. The amount of diffraction is greater for large and small openings. So, looking at = h / p, which diffracts more, an electron or you? An electron will seem more like a wave than you will.

Another moment of Duality Matter behaves as a wave and as a particle.

Dual Duality Matter and Light… both are waves and both are particles.

“Nobody understands quantum mechanics.” Richard Feynman Nobel Laureate, Physics “The more you see how strangely nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that.”

TOK Theoretical physicists have the job of predicting the results of experiments. In part this means that the classic question of “Why does that happen?” is no longer the primary job of scientists to answer. The pressing issues are “What will happen?” and “How can we use this?”

Review of Atomic Spectra

Is this an emission spectrum or an absorption spectrum?

All ‘bright line’ spectra are emission spectra.

This ‘dark line’ spectrum is from sunlight. The dark parts were absorbed by the atmosphere of the sun or the earth.

Review of Atomic Spectra Atoms emit light at the same frequencies (energies) that they absorb light. E = hf. When an atom absorbs light, an electron has jumped to a higher energy level. For example from level n = 1 to level n = 3. Different types of atoms (“elements”) have levels at different energies, so different elements emit and absorb different frequencies.

An electron in the 3 rd energy level. If an electron is in the 3 rd energy level, why can we see 3 frequencies of light? n = 3 to n = 1. n = 3 to n = 2, and n = 2 to n = 1.

The first few Electron Energy Levels of Hydrogen

Electron Energy Levels Energy levels are measured in electron Volts (eV). The values are negative (!). This is because 0 energy is the value of a free electron with no motion. Positive energies describe electrons that are free of an atom, and moving. Negative energies describe anything that is bound. The earth is bound to the sun, and electrons can be bound to a nucleus. The more negative the energy, the less energy it has.

Electron in a Box

Electron in a Box This is a theoretical idea that helps us understand quantum theory. The electron is bouncing back and forth in a one-dimensional box. The electron is considered to be like a standing wave, a probability wave. Since there is no probability of the electron being outside the box, the wave has nodes at the edges of the box.

Electron in a Box of length L. ‘n’ identifies the energy level n = 1 L = ( 1 / 2 ) n = 2 L = ( 2 / 2 ) n = 3 L = ( 3 / 2 ) L = ( n / 2 )

Electron in a Box L = ( n / 2 ) n = 2L / n Now add in the deBroglie idea: = h/p p = h / The momentum of the electron depends on which energy level the electron is in. p n = h / n p n = h / (2L / n) = nh/2L

Electron in a Box (use KE = p 2 /2m) p n = nh/2L E k = p 2 /2m E k = (nh/2L ) 2 /2m E k = n 2 h 2 /8mL 2 The energy of the electron is quantized. Quote from the IB syllabus: “Students should be able to show that the kinetic energy E K of the electron in the box is given by: E k = n 2 h 2 / 8m e L 2

Erwin Schrödinger (1926)

Schrödinger The big news is the nature of the wave that describes matter. Schrödinger figured out that the amplitude of the wave, the intensity of the wave, was related to the likelihood that a particle was in a location. The wave is a probability wave. The symbol for the probability wave is  (upper case),  (lower case). We spell it psi and pronounce it either as ‘see’ or ‘sigh.’

The wave function:  and its square   2 is the probability of finding the particle in a particular location at a particular time. For a hydrogen atom, there is a specific radius (about 0.5 x m) that is the most likely distance from the nucleus for an electron to be. The function  2 has a maximum at that location, but  2 is not zero anywhere!

Where is a particle in a box most likely to be?

Werner Heisenberg

Heisenberg Uncertainty Principle The HUP is regarded by many as the most fundamental idea in all of quantum mechanics. The HUP is about measurement and about knowledge (TOK). The HUP says that the more you know about one thing, the less you know about something else…

Heisenberg Uncertainty Principle  x  p ≥ h / 4  The uncertainty we have in measuring position (  x), times the uncertainty we have in measuring the momentum (  p) of the object when it is at that position, will always be greater than the Planck constant divided by 4 .

Heisenberg Uncertainty Principle  E  t ≥ h / 4  The uncertainty we have in measuring energy, times the uncertainty we have in measuring when the object had that energy, will always be greater than the Planck constant divided by 4 .

Heisenberg Uncertainty Principle Even with perfect equipment these uncertainties will be present. The act of measuring position will disturb the momentum, and vice versa. The act of measuring energy will always put limits on when the object had that energy.