Modern Physics Thanks to: Dr. P. Bertrand Oak Ridge HiS
Quantum Physics • Physics on a very small (atomic) scale is “quantized”. • Quantized phenomena are discontinuous and discrete, and generally very small. • Quantized energy can be throught of an 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 is a ray • We know from geometric optics that light behaves as a ray; it travels in a straight line. • When we study ray optics, we ignore the nature 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 studied this earlier in the year and we will use this equation again here. • C = f l • C: 3 x 108 m/s (speed of light in a vacuum) • f: frequency (Hz or s-1) • l: wavelength (m) (distance from crest to crest)
In quantum physics, we focus on how light behaves as a particle! • Light has a dual nature. In addition to behaving as a wave, it also behaves as 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”.
Calculating photon energy • The energy of a photon is calculated from the frequency of the light. • E = hf = hc / l because c = f l • E = nhf (for multiple n # of photons) • E: energy (J or eV) • h: Planck’s constant • 6.625 x 10-34 J s (SI system) • 4.14 x 10-15 eV s (convenient) • f: frequency of light (s-1, Hz)
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 of 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 x 10-19 J
Sample Problem What is the frequency and wavelength of a photon whose energy is 4.0 x 10-19 J? E = hf f = E/h = c = f l l = c/f =
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 = 4l86 J). • E = (104.2 kcal)(4186 J)( 1 mol ) • mol kcal 6.02x10 23mol’cls • E = 7.24 x 10-19 J = hf • f = 7.24 x 10-19 J/ 6.625 x 10-34Js • f = 1.09 x 1015 Hz ***
Atomic Transitions • 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? P = Etot /t E = hf P = n(hf)/t c = f l f = c/ l P = nh(c/ l) n = (P)(t)( l ) t (c)(h)
Solution Find total energy in one second from power P = W/t = E tot / t E tot = Pt = 3.0 x 10 -3 J Now see how many photons, n, will produce this energy E = hf (one photon) E tot = nhf (for n photons) E = nhc/ l (since wavelength is given and not frequency) 3.0x10-3 = n (6.625x10-34Js)(3.0x108m/s)/632.8x10-9m n = 9.55 x 1016
General Info re the Atom • Atoms are composed of • Nuclei (protons and neutrons) and electrons • When an atom encounters a photon • It usually ignores the photon, but sometimes absorbs the photon • If an atom absorbs a photon • The photon disappears and gives all its energy to the atom’s electrons
Quantized atomic 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.
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.
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 seen through hand held spectroscope
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. D E = -hf
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.
Photoelectric Effect #1 • Sample Problem
Question • 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 phenomenon is called the Photoelectric Effect.
Photoelectric Effect E = work function + K
Photoelectric Effect #2 • Sample Problem
Experimental determination of theKinetic Energy of a photoelectron
Photoelectric simulations • http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm • This is a link for a simulated photoelectric effect experiment • Another link: http://zebu.uoregon.edu/%7Esoper/Light/atomspectra.html • ***