Herriman High AP Physics 2 Chapter 27 Quantum Theory Herriman High AP Physics 2

Herriman High AP Physics 2 Section 27.2: The Photoelectric Effect and the Particle Theory of Light Light has a dual nature – it is made up of packets of energy called quanta or photons which are carried on a wave. When an atom absorbs energy electrons move from their normal or ground state to a higher energy or excited state. To go back to their ground state atoms give off this excess energy as light. Herriman High AP Physics 2

Herriman High AP Physics 2 The Energy of a Photon The energy of any photon of light given off in this way is determined by the equation: E = hf Where E = energy in joules h = 6.626 x 10-34 J•s (Planck’s Constant) f = frequency of the light Herriman High AP Physics 2

Section 27.2:The Photoelectric Effect The photoelectric effect is the ejection of photoelectrons from a material when light falls upon it. The material is sensitive to the frequency of the light not its intensity. This cutoff frequency, fc determines if electrons will be emitted. Herriman High AP Physics 2

Herriman High AP Physics 2 Photoelectric Effect The maximum kinetic energy of liberated photoelectrons is given by: Kemax = hf – Φ where Φ is called the work function of the material. This is measured in electron volts (eV). The cutoff frequency, fc occurs when hf = Φ so fc = Φ/h and since c = fλ the cutoff wavelength, λc = hc/Φ Herriman High AP Physics 2

Herriman High AP Physics 2 Sample Problem A sodium surface is illuminated with light of wavelength 0.3 µm. The work function of sodium is 2.46 eV. Calculate: The energy of each photon in electron volts The maximum kinetic energy of the ejected photoelectrons The cutoff wavelength for sodium. Herriman High AP Physics 2

Herriman High AP Physics 2 Solution c = fλ so f=c/λ = 3 x 108 m/s / 0.3 x 10-6 m = 1 x 1015 hz E = hf = (6.63 x 10-34 J●s)(1 x 1015 hz) = 6.63 x 10-19 J = 4.14 eV Kemax= hf – Φ = 4.14 eV – 2.46 eV = 1.68 eV Convert the work function, Φ = 2.46 eV, to Joules = 3.94 x 10-19 J λc = hc/Φ = (6.63 x 10-34 J●s)(3 x 108 m/s)/3.94 x 10-19 J =5.05 x 10-7 m Herriman High AP Physics 2

Section 27.6 The Dual Nature of Light and Matter Light has properties of both particles and waves. In 1924 Louis DeBroglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties. Using this idea DeBroglie connected the momentum of of photon to its wavelength. Herriman High AP Physics 2

Herriman High AP Physics 2 DeBroglie Since E = hf and E = mc2 E = hc/λ and p = E/c = hc/cλ By rearrangement: λ = h/p = h/mv Herriman High AP Physics 2

Herriman High AP Physics 2 Chapter 28 Atomic Physics Herriman High AP Physics 2

Early Models of the Atom Thompson’s Plum Pudding Model Rutherford’s Planetary Model Gold Foil Experiment Atom is mostly empty space Bohr Model Quantum Theory Herriman High AP Physics 2

Herriman High AP Physics 2 Atomic Spectra When a gas tube is electrified it gives off a set of frequencies of light that are dependent upon the gas in the tube. When examined with a spectrometer the resulting “bright lines” are called an emission spectrum. In addition radiating light of specific wavelength, an element can absorb specific wavelengths also. The spectral lines associated with this process are called the absorption spectrum. Herriman High AP Physics 2

Herriman High AP Physics 2 Chapter 29 Nuclear Physics Herriman High AP Physics 2

Herriman High AP Physics 2 Atomic Structure The Nucleus of an atom contains Protons – Positively Charged Neutrons – no charge Atomic Mass Number – denoted by the letter A, this number represents the total number of protons + neutrons in the nucleus, telling you what isotope of the element you have. Atomic Number – denoted by the letter Z, this number represents the number of protons in the nucleus, telling you what element you have. Herriman High AP Physics 2

Herriman High AP Physics 2 Nuclear Energy Atomic Symbol for a given isotope of an element is generally given as noted to the right. A prime example is an alpha particle or helium nucleus Herriman High AP Physics 2

Herriman High AP Physics 2 Nuclear Reactions Two Types of Nuclear reactions produce vast amounts of energy according to Einstein’s famous equation E = mc2 Fission – the splitting of an atom into smaller parts Fusion- the joining of two small nuclei to produce one larger nucleus Herriman High AP Physics 2

Section 29.2: Binding Energy Mass defect – is the amount of mass that is converted to energy during fission or fusion. Calculation of Mass defect is the difference between the actual mass of the atom and the known mass of each of its parts The amount of energy that this mass is converted into is called the binding energy Herriman High AP Physics 2

Herriman High AP Physics 2 Sample Problem Calculate the mass defect and energy released in the creation of Carbon-13. Solution Expected Mass: Protons = 6 (1.007276 u) = 6.043656 u Neutrons = 7(1.008665 u) = 7.060655 u 13.104311 u Known Mass -13.003355 u Mass Defect .100956 u Energy Released = (931.5 MeV/u)(0.100956 u) = 94.04 MeV Herriman High AP Physics 2

Section 29.3: Radioactivity Three types of Radioactivity Alpha – α – is the nucleus of a helium atom Can be stopped by a sheet of paper, is harmful only if ingested Beta – β – emission of an electron or positron Can be stopped by a sheet of lead, is harmful to all living tissue Gamma – γ – emission of a high energy photon Cannot be completely stopped. Very harmful to all living tissue. Herriman High AP Physics 2

Herriman High AP Physics 2 Nuclear Reactions Alpha Decay Beta Decay Gamma Emission Herriman High AP Physics 2

Herriman High AP Physics 2 Radioactive Decay Radioactive Decay is an exponential decay using the equation: 𝑁= 𝑁 0 𝑒 −λ𝑡 N is the amount of material present at time t N0 is the amount present at t=0. λ is the decay constant for the substance. Herriman High AP Physics 2

Herriman High AP Physics 2 Half Life The half life of a radioactive material is the amount of time required for ½ of the sample to decay into another element or isotope. Using the concept of half lives the earlier equation becomes: N = N0(½)n Where n is the number of Half lives that have occurred since time zero. Herriman High AP Physics 2

Herriman High AP Physics 2 Sample Problem Carbon-14, a radioactive isotope of carbon, has a half life of 5730 years. If a 20 gram sample of carbon-14 is allowed to decay for 10,000 years, how much remains at the end of this period? Herriman High AP Physics 2

Herriman High AP Physics 2 Solution a = a0(½)x a0 = 20 grams x = 10,000 yrs/5730 yrs/half life = 1.75 So a = 20 grams(½)1.75 = 5.95 grams Herriman High AP Physics 2

Nuclear Energy and Elementary Particles Chapter 30 Nuclear Energy and Elementary Particles Herriman High AP Physics 2

Applications of Nuclear Processes Energy can be released in a nuclear reaction by one of two processes: Fission – the splitting of a nucleus into smaller nuclei Fusion – the joining of two smaller nucleui into a larger nuclei Herriman High AP Physics 2

Herriman High AP Physics 2 Section 30.1: Fission Usually caused by neutron bombardment of the nucleus, causing the nucleus to split Mass is converted into energy All current nuclear reactor technology uses fission Fission is controlled by using a moderator, a material which absorbs neutrons to keep the chain reaction under control Herriman High AP Physics 2

Herriman High AP Physics 2 Section 30.2 Fusion Fusion reactions take lighter nuclei, often an isotope of hydrogen called deuterium and fuse them together to make a heavier nuclei, often helium This must occur at high energy and is very difficult to produce under laboratory conditions Currently no workable fusion reactor has been produced on earth The sun and stars all produce energy due to nuclear fusion Herriman High AP Physics 2