Exam 3 ReviewChapter 30 - Quantum PhysicsA blackbody is an object that perfectly absorbs and perfectly emits radiation. Thedistribution of frequencies in blackbody radiation only depends on the temperature(it does not depend on what the blackbody is made of).Light of frequency f consists of photons that each have an energy E = hf . Themore photons in a beam of light, the higher the intensity of the light.Photoelectric Effect:• A beam of light incident on a metal surface can cause electrons to be ejected.A single photon is responsible for each electron that is ejected.• The minimum amount of energy necessary to eject an electron is called thework function (W0). The energy of a photon must be at least as much as thework function to eject an electron. This defines a minimum frequency for theincoming light to eject an electron: f0= W0/h• If the energy of the incident photon is greater than the work function, theexcess energy goes into kinetic energy of the ejected electron. The maximumkinetic energy the ejected electron can have is given by Kmax= hf − W0.• Increasing the intensity of the incident light means more photons hit the metalper second, thus more electrons can be ejected.Remember the momentum of a photon is given by p = E/c = h/λ.When an X-ray photon undergoes a collision with an electron initially at rest, thephoton is scattered, changing its direction and energy. (Since the energy of the pho-ton changes, so does the wavelength and frequency.) The change in the wavelength1(difference in the wavelength before and after the collision) can be calculated giventhe scattering angle of the photon, θ. Energy and momentum are conserved in thisinteraction.Light can exhibit both wave-like and particle-like properties. Particles can alsoexhibit wave-like properties. The de Broglie wavelength of a particle is given byλ = h/p. The de Broglie wavelengths of everyday objects, like people and baseballs,is so small that we don’t notice the wave-like properties of these objects. The deBroglie wavelength of an electron is large enough that the wave-like properties playa noticeable role in atomic systems.The Heisenberg Uncertainty Principle states that there is a lower limit on the prod-uct of the uncertainties in a particle’s position and momentum (not the position andmomentum themselves, but in the uncertainties in those quantities). This meansthe uncertainties are inversely related. The more precisely the momentum is known(small ∆p), the larger the uncertainty on the position (large ∆x) and vice versa.Chapter 31 - Atomic PhysicsThe Bohr Model of the Hydrogen Atom:• The electron in a hydrogen atom orbits the nucleus.• Only certain orbits are allowed. The orbits are labeled by a single quantumnumber n = 1, 2, 3, ...• When an electron changes from one allowed orbit to another, a photon is emit-ted or absorbed, with the frequency of the photon determined by the differencein energy of the orbits: ∆E = hf = hc/λ. This explains the spectral lines inhydrogen.• The Bohr Model can be used for any atom with atomic number Z, if there isonly one electron orbiting the nucleus.• The energy of a Bohr orbit: En= (−13.6eV)Z2/n2. (Note the negative sign!)The ground state of hydrogren has an energy of -13.6 eV. The n = ∞ statehas an energy of 0 eV.2• n = 1 is the ground state. n = 2 is the first excited state, n = 3 is the secondexcited state, and so on.The Quantum Mechanical Model of the Hydrogen Atom: The state of a hydrogrenatom requires four quantum numbers.• n = 1, 2, 3, ...• ` = 0, 1, 2, 3, ...n − 1• m`= −`, −` + 1, −` + 2, ... − 1, 0, 1, ...` − 2, ` − 1, `• ms= ±(1/2)The Quantum Mechnical Model of a Multielectron Atom:• The Pauli Exclusion Principle says no two electrons can occupy the same state(have the same set of quantum numbers).• The ground state of a multielectron atom corresponds to all of the lowest energylevels being filled with electrons.• The maximum number of electrons that can occupy a subshell is given by2(2` + 1).• The electronic configuration indicates the arrangement of the electrons. Thenotation for each level is: n[letter for `]number of electrons in this subshellChapter 32 - Nuclear Physics and Nuclear Radia-tionThe species of nucleus is determined by the number of protons. A nucleus with thesame number of protons, but different number of neutrons is called an isotope.E = mc2means mass is a form of energy. In nuclear reactions, any change in massmust be taken into account to conserve energy. We can write mass in terms ofMeV/c2. A mass of 1 MeV/c2has an energy equivalent of 1 MeV.Remember an alpha particle is a helium nucleus:42He.3In beta decay, if the daughter nucleus has one more proton than the parent nucleus,an electron is emitted. If the daughter nucleus has one less proton than the parentnucleus, a positron is emitted. (This is due to conservation of charge - the charge onthe right hand side must be equal to the original charge, +Ze.)AZX →AZ+1Y + e−+ ¯νe(1)AZX →AZ−1Y + e++ νe(2)The energy released in a nuclear interaction is the energy that’s left over once themass energy is taken into account:E = ∆mc2= (mf− mi)c2If a substance is radioactive, the amount of the substance remaining will decreaseover time, as will the activity (decays/s). The half-life is the amount of time it takesfor the amount of the substance (or the activity) to be reduced to one-half its originalvalue. After two half-lives, (1/2)*(1/2) = 1/4 remains, and so. Don’t confuse thehalf-life with the decay constant, which has units of inverse time.Nuclear binding energy is the energy it would take break the nucleus apart into theindividual protons and neutrons. It is given by the difference in mass of the nucleusand the sum of the individual proton and neutron masses. If you are given the atomicmass, you have to subtract off the mass of the electrons to get the mass of just thenucleus.The rad radiation unit gives the amount of energy deposition of radiation. But itdoesn’t say anything about the effect of radiation on tissue, as different types ofradiation cause different amounts of damage. However, the rem radiation unit takesinto account the different effects of different types of radiation. A radiation dose of1 rem does the same amount of damage no matter what kind of radiation.dose in rem = dose in rad x RBE (where RBE is different for different types ofradiation)Chapter 16 - Temperature and HeatThe size of one degree