Physics – Modern Physics - Quick Guides

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Study GuidePhysics–Modern Physics1.Quantum MechanicsClassical physics works well for everyday objects, but it fails in two major areas:•Objects moving close to the speed of light•Matter at the atomic and subatomic scaleTo understand howatoms, molecules, and nucleibehave, scientists developedquantummechanics. This branch of physics explains phenomena that classical mechanics cannot.1.Blackbody RadiationAblackbodyis an ideal object with two special properties:•It absorbsallradiation that falls on it.•It emits radiation perfectly when heated.When scientists studied how the intensity of radiation varies with wavelength, they found thatclassical physics could not explain the results.2.Planck’s SolutionIn 1900,Max Planckproposed a revolutionary idea. To match experimental data, he made two keyassumptions:1.Energy is quantizedMolecules can only have specific energy values, not any value. These energy levels are given by:[E = hf]where:

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Study Guide○(n) is a quantum number (1, 2, 3, …)○(f) is frequency2.Energy is emitted in packetsEnergy is released in small bundles calledquanta, now known asphotons.The energy of each photon is:[E = hc/λ]Why This Was ImportantThis idea was radical because it treated energy asdiscrete packetsinstead of a smooth, continuousflow. A molecule can only change its energy if it absorbs or emitsexactly one quantumof energy.3.Photoelectric EffectThephotoelectric effectoccurs when light shines on certain metals and causes electrons to beejected. These electrons are calledphotoelectrons.Scientists noticed several surprising results:•Each metal requires aminimum frequencyof light, called thethreshold (cutoff) frequency•Increasing lightintensitydoesnotincrease the electrons’ kinetic energy

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Study Guide•Increasing lightfrequencyincreases the electrons’ maximum kinetic energy•Electrons are emittedalmost instantly, even at low intensities4.Einstein’s ExplanationAlbert Einstein explained thephotoelectric effect using Planck’s quantum idea and energyconservation. He proposed the equation:[K.E.max= hf–Q]Where:•(hf) is the energy of the incoming photon•(Q) is thework function(minimum energy needed to remove an electron from the metal)What This Means•If the photon energy isless than (Q)→ no electrons are emitted•Extra photon energy becomeskinetic energyof the electron5.Explaining the Observations•Athreshold frequencyis required because each photon must carry enough energy•Higherintensitymeans more photons → more electrons, but same kinetic energy•Higherfrequencymeans more energetic photons → faster electrons•Even low-intensity light can eject electrons immediately if frequency is high enough

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Study Guide6.Compton ScatteringMore evidence for quantum behavior came from theCompton effect, discovered byArthurCompton.In this effect:•A high-energyX-ray photoncollides with an electron•The scattered photon loses energy and gains alonger wavelengthThis change can be explained only if the photon behaves like aparticlewith momentum.Key Features•Energy and momentum conservation apply (like billiard-ball collisions)•The wavelength shift depends on thescattering angle•The effect is noticeable only forhigh-energy photons, such as X-rays7.Particle–Wave DualityExperiments like the photoelectric and Compton effects show thatlight behaves as both a waveand a particle.•High-energy photons(short wavelength, e.g. X-rays) behave more like particles•Low-energy photons(long wavelength, e.g. radio waves) behave more like wavesBoth models are necessary to fully describe electromagnetic radiation.8.De Broglie WavesLouis de Broglie suggested a bold idea:If light (a wave) can act like a particle, thenparticles might also behave like waves.

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Study GuideImportant Note•De Broglie wavelengths areextremely smallfor everyday objects•Because Planck’s constant is very tiny((10^{-34})), wave effects are noticeable only for verysmall particles like electrons9.Heisenberg Uncertainty PrincipleTheHeisenberg uncertainty principlestates that it is impossible to measure both:•theexact position, and•theexactmomentumof a particle at the same time.

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Study Guide2.Atomic Structure1.Quantization of Angular MomentumBohr proposed that electrons can move only in certain allowed circular orbits around the nucleus. Inthese orbits, theangular momentumof the electron is quantized, meaning it can take only specificvalues:Here:•(n) is an integer called theprincipal quantum number•(h) is Planck’s constantThis condition restricts electrons to specific orbits and is a key idea of the Bohr model.2.Radius ofElectron OrbitsBohr calculated the radius of each allowed orbit by equating:•theelectrostatic force(from Coulomb’s law), and

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Study Guide•thecentripetal forceneeded to keep the electron in circular motionThis leads to the expression:When (n = 1), the radius is called theBohr radius.This is thesmallest possible orbitin the hydrogen atom.3.Energy of an Electron in the Hydrogen AtomThe total energy of an electron is the sum of:•Kinetic energy, and•Potential energyAfter substituting values from Bohr’s equations, the total energy depends only on the quantumnumber (n).4.Ground State and Ionization Energy•When (n = 1), the electron is in theground state•The ground-state energy of hydrogen is–13.6 eV

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Study GuideThis value matches theionization energyof hydrogen—the energy required to completely removethe electron from the atom.This excellent agreement strongly supported Bohr’s model.5.Emission of Radiation and Energy TransitionsWhen an electron jumps from a higherenergy level to a lower one, it emits a photon. According toBohr’s second postulate:[hf = Ef-Ei]Substituting the energy expressions gives:Using the relation (c = fλ), this becomes:6.The Rydberg ConstantFrom the above equation, theRydberg constantis identified as:

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