Quantum Physics • Physics on a very small (e.g., atomic) scale is “quantized”. • Quantized phenomena are discontinuous and discrete, and generally very small. • Quantized energy can be thought of as existing in packets of energy of specific size. • Atoms can absorb and emit quanta of energy, but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.
Light: 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.
Light: Wave • We will frequently use one equation from wave optics in quantum optics. • c = λf • c: 3 x 108m/s (the speed of light in a vacuum) • λ: wavelength (m) (distance from crest to crest) • f: frequency (Hz or s-1)
Light: 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, or at very high light energies. • A particle of light is called a “photon”.
Photon Energy • The energy of a photon is calculated from it the frequency of the light. • E = hf • E: energy (J or eV) • h: Planck’s constant • 6.625×10-34 J s • 4.14 ×10-15 eV s • f: frequency of light (s-1, Hz)
Check • Which has more energy in its photons, a very bright, powerful red laser or a small key-ring red laser? • Which has more energy in its photons, a red laser or a green laser?
Electron Volts • 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
Problem • What is the frequency and wavelength of a photon whose energy is 4.0 x 10-19 J?
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?
Energy Levels • This graph shows allowed quantized energy levels in a hypothetical atom. • The more stable states are those in which the atom has lower energy. • The more negative the state, the more stable the atom.
Energy Levels • The highest allowed energy is 0.0 eV. Above this level, the atom loses its electron. This level is called the ionization 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.
Energy Levels • Transitions of the electron within the atom must occur from one allowed energy level to another. • The electron CANNOT EXIST between energy levels.
Photon Absorption • 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.
Photon Absorption • When a photon is absorbed, it excites the atom to higher quantum energy state. • The increase in energy of the atom is given by ΔE = hf. 0eV -10eV
Absorption Spectra • 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 Spectra • Absorption spectra always involve atoms going up in energy level. 0eV -10eV
Photon Emission • 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.
Photon Emission • When a photon is emitted from an atom, the atom drops to lower quantum energy state. • The drop in energy can be computed by ΔE = hf. 0eV -10eV
Emission Spectra • 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 • Emission spectra always involve atoms going down in energy level. 0eV -10eV
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.
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.
Problem • The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum? Draw the transitions.
Absorption • 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.
Extra Energy • Now, suppose a photon with TOO MUCH ENERGY encounters an atom? • If the atom is “photo-active”, a very interesting and useful phenomenon can occur… • This is called the Photoelectric Effect.
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.
Photoelectric Effect • Photon Energy = Work Function + Kinetic Energy • hf = Ф + Kmax • Kmax = hf – Ф • Kmax: Kinetic energy of “photoelectrons” • hf: energy of the photon • Ф : binding energy or “work function” of the metal.
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?
Photoelectric Effect • Suppose you collect Kmax and frequency data for a metal at several different frequencies. You then graph Kmax for photoelectrons on y-axis and frequency on x-axis. What information can you get from the slope and intercept of your data?
The Photoelectric Effect • 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 (which is controlled by the scientist), and measuring the resulting 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 • 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.
Photoelectric Effect • 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.
Mass of a Photon • Photons do not have “rest mass”. They must travel at the speed of light, and nothing can travel at the speed of light unless its mass is zero. • A photon has a fixed amount of energy (E = hf). • We can calculate how much mass would have to be destroyed to create a photon (E=mc2).
Problem • Calculate the mass that must be destroyed to create a photon of 340nm light.
Photon Momenum • Photons do not have “rest mass”, yet they have momentum! This momentum is evident in that, given a large number of photons, they create a pressure. • A photon’s momentum is calculated by
Proof of Photon Momentum • Compton scattering • Proof that photons have momentum. • High-energy photons collided with electrons exhibit conservation of momentum. • Work Compton problems just like other conservation of momentum problems • except the momentum of a photon uses a different equation.
Problem • What is the momentum of photons that have a wavelength of 620 nm?
Problem • What is the frequency of a photon that has the same momentum as an electron with speed 1200 m/s?
Matter Waves • 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)
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 photon’s energy is calculated using its frequency • E = hf
Momentum • For a particle that is moving • p = mv • For a photon • p = h/λ • Units?
Wavelength • For a photon • λ = c/f • For a particle, which has an actual mass, this equation still works • λ = h/p where p = mv • This is referred to as the deBroglie wavelength
Matter Wave Proof • Davisson-Germer Experiment • Verified that electrons have wave properties by proving that they diffract. • Electrons were “shone” on a nickel surface and acted like light by diffraction and interference.
Problem • What is the wavelength of a 2,200 kg elephant running at 1.2 m/s?