Unit 16: Quantum and Nuclear Physics
Light behaving like particles, matter behaving like waves, an atom that only glows at a few exact colors, and a nucleus trading mass for energy.
12 topics · 44 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Blackbody Radiation
- How it worksHow did Planck's assumption that light energy comes in discrete packets finally explain a hot object's whole glow spectrum?
- Common mistakeWhy doesn't classical physics, which predicted infinite energy at short wavelengths, actually describe a hot object's real glow?
- Ties togetherHow does Planck's quantized light energy set up the very idea Einstein later used to explain the photoelectric effect?
Your turn1 of 2
Classical physics predicted that a hot object should radiate infinite energy at very short wavelengths, the 'ultraviolet catastrophe,' but real hot objects clearly don't. What resolved this contradiction?The Photoelectric Effect
- How it worksHow does treating light as individual photons, each with energy set only by frequency, explain the photoelectric effect completely?
- Worked exampleFind the kinetic energy of an electron ejected by an 8 times 10 to the 14 Hz photon from a metal with a 2 eV work function.
- Common mistakeWhy isn't a photon's energy determined by how intense or bright the overall light beam happens to be?
- Going furtherWhat happens to the number of electrons ejected per second, as opposed to their energy, when the light's intensity is raised?
- Worked exampleFind the threshold frequency below which no electrons are ejected from a metal with a work function of 2.3 eV.
Your turn1 of 2
A metal has a work function of 2 eV. Write the kinetic energy of an ejected electron as a function of f, the photon frequency in units of 1014 Hz. Use h = 4.136x10−15 eV s.The Compton Effect
- How it worksHow does treating a photon as a particle with momentum, colliding with an electron like a billiard ball, explain that wavelength shift?
- Worked exampleFind the wavelength shift of an X-ray photon scattered at 90 degrees off a free electron.
- Ties togetherHow does the Compton effect confirm the very same particle picture of light the photoelectric effect first suggested?
Your turn1 of 2
Find the wavelength shift of an X-ray photon scattered at 121 degrees off a free electron. Use h/(me c) = 2.43x10−12 m.The Bohr Model of the Hydrogen Atom
- How it worksHow did Bohr's model quantize the electron's allowed orbits into discrete energy levels to explain hydrogen's spectral lines?
- Worked exampleFind the energy of a photon emitted when a hydrogen electron drops from the n=3 level to the n=2 level.
- Common mistakeWhy doesn't a hydrogen electron sitting in an allowed Bohr orbit continuously radiate energy and spiral into the nucleus?
- Going furtherWhat happens to the spacing between hydrogen's energy levels as the quantum number n keeps getting larger?
Your turn1 of 2
Find the energy of a photon emitted when a hydrogen electron drops from the n=5 level to the n=2 level.De Broglie Matter Waves
- How it worksHow does de Broglie's hypothesis assign every moving particle a wavelength set by its own momentum?
- Worked exampleFind the de Broglie wavelength of an electron moving at 2 times 10 to the 6 m/s.
- Going furtherWhat happens to a thrown baseball's de Broglie wavelength compared to an electron's, given its far larger mass?
Your turn1 of 2
Find the de Broglie wavelength of an electron moving at 7 times 106 m/s. Use h = 6.626x10−34 J s and electron mass m = 9.11x10−31 kg.Wave-Particle Duality
- How it worksHow does each individual photon land at a random spot while the pattern accumulated over many photons reveals wave interference?
- Worked exampleFind how a double-slit setup's slit separation and screen distance should be chosen to show visibly separated fringes for electrons of a given de Broglie wavelength.
- Common mistakeWhy doesn't watching a single photon land on the screen ever look anything like a wave striking that screen?
- Ties togetherHow does this single-photon buildup connect de Broglie's matter waves directly back to Young's original light experiment?
Your turn1 of 2
Photons are fired through a double slit one at a time, so far apart that only one photon is ever in the apparatus at once. Over a long exposure, does an interference pattern still build up on the screen?The Quantum Atom and the Periodic Table
- How it worksHow do allowed electron shells and the exclusion principle together build up the periodic table one element at a time?
- Common mistakeWhy isn't an atom's electron structure just every electron falling into the single lowest energy state at once?
- Going furtherWhat happens to an atom's chemical behavior once its outermost electron shell is completely filled?
Your turn1 of 2
Why can't two electrons inside the same atom ever occupy exactly the same quantum state?Nuclear Structure and Binding Energy
- How it worksHow does a nucleus's missing mass convert, through E equals m c squared, into the binding energy holding it together?
- Worked exampleFind the binding energy of a nucleus with a mass defect of 0.03 atomic mass units.
- Common mistakeWhy doesn't a stable nucleus fly apart under the mutual electric repulsion between all its own protons?
- Going furtherWhat happens to the binding energy per nucleon as you move from light nuclei up toward iron on the periodic table?
Your turn1 of 2
Find the binding energy of a nucleus with a mass defect of 7 times 0.01 atomic mass units. Use 1 amu = 931.5 MeV/c2.Radioactivity and Decay Modes
- How it worksHow do alpha, beta, and gamma decay each change a nucleus's mass and charge in their own distinct way?
- Worked exampleFind the resulting element and mass number after a uranium-238 nucleus undergoes alpha decay.
- Common mistakeWhy isn't beta decay simply an electron that was already sitting inside the nucleus being ejected outward?
- Going furtherWhat happens to a nucleus's identity as it moves through a whole chain of alpha and beta decays in a row?
- Worked exampleFind the resulting element and mass number after a carbon-14 nucleus undergoes beta-minus decay.
Your turn1 of 2
A nucleus with mass number 235 and atomic number 90 undergoes alpha decay. Find the atomic number of the resulting nucleus.Half-Life and the Radioactive Decay Law
- How it worksHow does a constant decay probability per atom produce a smooth exponential decline across a whole sample?
- Worked exampleFind how much of a 100 gram sample with a 5 year half-life remains after 20 years.
- Worked exampleFind the decay constant of an isotope with a half-life of 8 days.
- Going furtherWhat happens to a radioactive sample's decay rate as more and more of that sample decays away over time?
Your turn1 of 2
A sample of 142 grams has a half-life of 7 years. Write the amount remaining as a function of t, the elapsed time in years.Nuclear Fission
- How it worksHow does a neutron striking a uranium-235 nucleus split it into two smaller nuclei plus free neutrons that keep the reaction going?
- Worked exampleFind the energy released by a fission event with a mass defect of 0.2 atomic mass units.
- Ties togetherHow does nuclear fission release energy from the very same binding-energy-per-nucleon curve you'd use to compare element stability?
Your turn1 of 2
Find the energy released by a fission event with a mass defect of 4 times 0.1 atomic mass units. Use 1 amu = 931.5 MeV/c2.Nuclear Fusion
- How it worksHow does fusing light nuclei like hydrogen into helium release energy from the opposite end of the same binding-energy curve fission uses?
- Common mistakeWhy does building a working fusion reactor on Earth turn out to be so much harder than sustaining fusion inside the Sun's core?
- Ties togetherHow do fission and fusion end up releasing energy from opposite ends of the very same binding-energy-per-nucleon curve?
Your turn1 of 2
The Sun continuously fuses hydrogen into helium in its core, releasing energy for billions of years. Why is building a controlled, net-energy-positive fusion reactor on Earth so much harder than what happens naturally inside the Sun?