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Foundations for quantum mechanics Photoelectric Effect Some background Imagine heating an iron bar with, say, an induction heater. For example, here. Color of heated objects When you heat an object, it glows. The color depends on the temperature. Hypothesis: Temperature is a measure of the random kinetic energy of particles that make up a substance. Moving electric charges emit electromagnetic waves. reasonable to expect fastermoving charges emit more energetic (higher frequency) waves. Hypothesis tested Wilhelm Wien investigated the relationship between temperature of blackbody emitter to peak wavelength (1893) 1 𝑚𝑎𝑥 𝛼 𝑇 (𝐾) temperature peak wavelength peak frequency Oops… Classical physics predicted a much more intense peak than what was actually observed at low wavelengths. This was called the “ultraviolet catastrophe”. Quantization of light In 1901, Max Planck proposed an math trick as a solution. Also quantized: matter (atoms), standing waves on oscillating string, etc. Assume light comes in tiny but discrete packets of energy, known as ‘quanta’ 𝐸 = ℎ𝑓 where 𝐸 = energy of photons ℎ = proportionality constant, = 6.63 x 10-34 Js 𝑓 = frequency of light Implications Reasons to trust the model + describes observed blackbody spectra perfectly Reasons to question the model - Requires light to come in chunks (??) - How do you explain diffraction? - How do you explain interference? - How do you explain polarization? Photoelectric Effect Hertz (1887) discovered that when you shine a light on a metal surface, it can generate a current (i.e., some electrons are knocked loose). If you are clever, you can measure how much current. Pro tip: Put a metal plate and an electrode in an evacuated glass tube and measure the current produced when you shine a light on the plate. Wilhelm Hallwachs(1888) discovered that the leaves of a neutrally-charged electroscope will separate when the plate to which they are attached is exposed to ultraviolet light. Photoelectric Effect If you are especially clever, you can measure how much kinetic energy those electrons have. Put a voltage source in the circuit and switch the direction the current flows. Adjust the voltage until the current drops to zero. KEmax = eV0 Where V0 = amount of energy to stop electrons (verified by ammeter), called ‘stopping potential’ Experiment some… Use the PHeT simulator to experiment. 1) Explore the impact of changing the intensity of the light. 2) Explore the impact of changing the color of the light. 3) Explore the impact of changing the type of material. 4) Explore the impact of changing the voltage of the battery. Patterns: 1 of 2 Experiment Results Analysis Current vs. intensity of light intensity current Stopping potential vs. frequency of light frequency stopping potential, -V0 Patterns: 2 of 2 Experiment Current vs. voltage difference Current vs. voltage difference, with more intense light Results Analysis voltage current, then levels off voltage current, then levels off at a higher level. V0 does not change. Worth noting: ~0 s lag time between light hitting surface and current flowing Energy in waves In waves, the height (more properly, the amplitude) of the wave determines its energy. Patterns & Explanations Pattern current intensity Wave-based Explanation current levels off with changing voltage difference Electrons require some minimum amount of energy to be released. Electrons absorb enough energy from light to be ejected from metal. Patterns & Explanations Pattern Well-defined stopping potential, regardless of intensity Wave-based Explanation Below certain frequency, no current at all High-intensity red light releases no electrons. Low-intensity blue light does. More intense = more energy Should be harder to stop electrons liberated by more intense light; it is NOT. Making sense of photoelectric effect Einstein’s insight: Planck addressed ultraviolet catastrophe by hypothesizing that energy is emitted in discrete quanta. What if energy is only absorbed in discrete amounts? Patterns & Explanations Pattern current intensity Wave-based Explanation Electrons absorb enough energy from light to be ejected from metal. Electrons absorb enough energy from light to be ejected from metal. current levels off with changing voltage difference Electrons require some minimum amount of energy to be released. Electrons require some minimum amount of energy to be released. Particle-based Explanation Patterns & Explanations Pattern Well-defined stopping potential, regardless of intensity Wave-based Explanation Particle-based Explanation More intense = more energy Should be harder to stop electrons liberated by more intense light; it is NOT. Electrons absorb energy from individual photons, the quanta of light. Below certain frequency, no current at all High-intensity red light releases no electrons. Low-intensity blue light does. If an individual photon at a particular wavelength does not have sufficient energy to release an electron, neither will any number of similar photons. What we learned… 1) Some frequencies of light do not have enough energy to liberate electrons. 2) Energy is conserved. If light has enough energy to liberate an electron, excess energy makes the electron move faster. 3) Increasing frequency of light increases maximum kinetic energy linearly. Photoelectric effect 𝐾𝐸𝑚𝑎𝑥 = ℎ𝑓 − 𝜑 for values of hf > 𝜑 Where 𝐾𝐸𝑚𝑎𝑥= peak kinetic energy of released electrons ℎ 𝑓 𝜑 = Planck’s constant, 6.63 x 10-34 Js = frequency of light [Hz or s-1] = work function of metal = the least amount of energy required to knock an electron off an atom, varies from small to very, very small Test While attempting to disprove photon hypothesis in 1913-14, Millikan confirmed it instead. Implications The model describing light as a wave does not work to describe photoelectric effect. The model describing light as a particle does not work very well to describe polarization or diffraction. Light behaves like a wave and a particle. Particles and inference? If you shine a bright light through double slits, you expect a familiar interference pattern to form. Photons and inference? What happens if you send a stream of photons through the double slits one at a time? Classically, you would expect the “particle” to go through one slit or the other. Sensor after very few photons have passed through double slits Sensor after ~105 photons have passed through double slits Sensor after ~109 photons have passed through double slits Sensor after many photons have passed through double slits Photons and inference? What happens if you send a stream of photons through the double slits one at a time? Classically, you would expect the “particle” to go through one slit or the other. Instead, individual photons interfere with themselves (?!) Example