Modern Physics Overview
History ~1850s Classical (Newtonian) mechanics could not explain the new area of investigation atomic physics Macro vs Micro New field of Quantum Mechanics, focused on explaining the behavior of molecules, atoms and nuclei Who were the main players? Planck Hertz De Broglie Einstein
Planck s Observations Quantum Mechanics Light exists in discrete bundles of energy called photons Energy of one quanta of light ( photon ) with frequency (f) and wavelength ( ) is: E = h*f, or E = h*c/, where h = Planck s constant = 6.63 x 10-34 J.s, and c = speed of e/m radiation (light) in vacuum = 3 x 10 8 m/s Energy of multiple (n) photons E = n(h*f) Units Joules or electron-volts (ev), where 1 ev = 1.6 x 10-19 J h = 4.14 x 10-15 ev after conversion Remember: watch the units for Planck s constant! Convert from J to ev (or v/v) if necessary! Planck s constant
Example of Planck s formula How much energy (E) is emitted from a light source vibrating at a frequency of 4.5 x 10 14 Hz? (Joules and ev) E = hf E (joules) = (6.63 x 10-34 )(4.5 x 10 14 ) E = 2.98 x 10-19 J, or E (ev) = (4.14 x 10-15 ) (4.5 x 10 14 ) ev E = 1.86 ev
De Broglie s Waves DeB asked Why just light? He proposed that any particle of mass (m) moving with a velocity (v) has an associated wavelength (λ), defined by: h λ (h = 6.63 x 10-34 J.s) mv This is De Broglie s wavelength For example
Example of De Broglie s formula What is the wavelength (λ) of a proton (mass = 1.67 x 10-27 kg) traveling at 3 x 10 8 m/s? Solve using DeB s formula λ = h/mv λ = 6.63 x 10-34 / (1.67 x 10-27 )(3 x 10 8 ) λ = 1.32 x 10-15 m What about a baseball (m=0.145 kg and v=45 m/s) λ = 1.02 x 10-34 m
Models of Light what is light? Particle characteristics (Newton) Photoelectric effect Photon momentum (collisions) Wave characteristics (Huygens) Reflection Refraction, etc Wave-Particle Duality! Newton/Einstein vs Young/Hertz/Maxwell
Visible Light & Planck s Formula E = hf Color Wavelength Frequency Energy Red Longer Lower Lower Violet Shorter Higher Higher Photons of higher frequency have more energy than those of lower frequency
Photoelectric Effect - History Hertz (1880s) hypothesized, from experiments, that when certain metals were hit by UV radiation, electrons must be released, and coined the term photoelectric effect Einstein tied Hertz s work with Planck s investigations and developed the theory of photoelectric effect for which he won the Nobel Prize in 1921
P/E Effect in the wild! Solar racer & calculator
Photoelectric Effect - Overview Photons
Photoelectric Effect? The incoming light photon has energy (E = hf) and strikes a metal surface. If the frequency of the photon is greater than the threshold frequency of the metal, then an electron will be emitted.
Photoelectric Effect KE electron = Energy photon - Work fn metal KE = h*f - W, where W = h*f t (f t = threshold frequency for the metal) The threshold frequency (f t ) reflects the work function (W) of the metal being irradiated KE e E ph Perhaps? W
Photoelectric Effect (E vs W) If E photon < Work function (photon freq < threshold freq) E photon = Work function (photon freq = threshold freq) E photon > Work function (photon freq > threshold freq) Then No atomic change Electrons are dug out and sit at the metal surface Electrons are dug out and are released from the metal as current
Selected Work Functions Metal Work Function (ev) Aluminum 4.08 Beryllium 5 Cesium 2.1 Cobalt 5 Selenium 5.11 Sodium 2.28 Zinc 4.3
Practice Each photon of yellow light carries an energy of 2.5 ev. What is the frequency (f) and wavelength (λ) of the light? Solve E = h*f for f f = E/h = 2.5/(4.14 x 10-15 ) f = 6.04 x 10 14 hz Solve c = λ*f for λ c = λ x f > 3 x 10 8 = λ x 6.04 x 10 14 λ = 4.97 x 10-7 = 497 nm
Practice A photocell has a work function of 2.7eV. What must be the threshold frequency of the light shining on the photocell? Solve W = h*f t for f t 2.7 = (4.14 x 10-15 ) * f t f t = 6.51 x 10 14 Hz Note: ev version of h used in calculations!
Practice The work function of silver is 4.73 ev. EM radiation with a frequency of 1.2 x 10 15 Hz strikes pure silver. What is the speed (v) of the electrons (m=9.11 x 10-31 kg) emitted? Solve KE = h*f W, then v using KE = ½ mv 2 KE = hf W KE = (4.14E-15)(1.2E15) 4.73eV KE = 0.238 ev > (convert ev to J) = 3.81E-20 J KE = ½ mv 2 3.81E-20 = ½ (9.11E-31) * v 2 v = 2.89E5 m/s
Energy Levels Bohr Atom Model Neils Bohr (1913) proposed: Electrons orbiting a nucleus radiate light when they change orbits, not when they are in orbit! Electrons can change orbit only when they absorb or emit energy Orbits are quantized (integer values)
Energy level diagrams (ELD) ELDs show allowed energy states for the electrons of an atom If an electron absorbs a photon it becomes excited and jumps up an energy level. When the electron drops to a lower state it emits 1 or more photons. ELD for hydrogen
Practice on ELDs Using the hydrogen ELD in your notes: How much energy is required for an electron to jump from n=1 to n=4? 12.75 ev from n=2 to n=5? 2.86 ev If an electron @ n=1 (ground state) receives 13.10 ev of energy, where does it finish? receives 13.05 ev of energy, where does it finish? How much energy does an electron emit (in a photon) when dropping from n=6 to n=2? n=5 3.4 ev n=4
Radioactivity 1896 Becquerel discovered radiation from a uranium sample Nobel Prize in 1903 Rutherford described the radiation and coined the terms alpha, beta and gamma radiation Radioactivity? Nuclei of uranium and many other isotopes are unstable and spontaneously transform themselves (decay) into other nuclei 238 92U ----> 4 2He + 234 90 Th 32 15P ----> 0-1e + 32 16S Ex. Carbon-12 = ~99%, Carbon-14 = ~1%
Radioactivity Half-life = amount of time for ½ the current mass to decay
Radioactivity in Everyday use Medical X-rays, scans Engineering Metal fatigue Military Fission/fusion History Carbon dating
Radioactivity Formulas Activity (decay rate) in Bequerel (Bq) Act = N/ t = change in # of atoms (N) over time (t), or Act = - N where = decay constant, and N = number of atoms in a sample Half-Life formula T 1/2 = 0.693/ Population Formula N = N 0 e - t, where N 0 = original sample of atoms t = time period later N = atoms remaining after time (t) N/N 0 = e - t is the fraction left after the decaying period e - t
Practice A sample of Cobalt-60, with a half-life of 5.26 years, containing 5 x 10 12 radioactive atoms is stored for 10 years. How many Co-60 atoms remain after this time? Solve N = N o e -λt for N after finding λ (decay) λ = 0.693/T 1/2 = 0.132 N = 5 x 10 12 x e (-0.132 x 10) N = 1.33 x 10 12 atoms