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Exercícios de relatividade, quântica e nuclear · Physics Playground

ExercíciosFísica

Relatividade, quântica e nuclear

56 problemas com soluções resolvidas, de Physics e College Physics.

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Aprenda antes: Relatividade Restrita, Fótons e Níveis de Energia, Radioatividade e Energia Nuclear, Partículas e o Modelo Padrão

Physics10.1 Postulates of Special Relativity

ExemploCalculating the Time it Takes Light to Travel a Given DistanceThe sun is 1.50 × 108 km from Earth. How long does it take light to travel from the sun to Earth in minutes and seconds?

Physics10.2 Consequences of Special Relativity

ExemploThe Speed of LightOne night you are out looking up at the stars and an extraterrestrial spaceship flashes across the sky. The ship is 50 meters long and is travelling at 95 percent of the speed of light. What would the ship’s length…

Physics21.1 Planck and Quantum Nature of Light

ExemploHow Many Photons per Second Does a Typical Light Bulb Produce?Assuming that 10 percent of a 100-W light bulb’s energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, calculate the number of visible photons emitted per second.
ExemploHow does Photon Energy Change with Various Portions of the EM Spectrum?Refer to the Graphs of Blackbody Radiation shown in the first figure in this section. Compare the energy necessary to radiate one photon of infrared light and one photon of visible light.

Physics21.2 Einstein and the Photoelectric Effect

ExemploPhoton Energy and the Photoelectric Effect: A Violet Light(a) What is the energy in joules and electron volts of a photon of 420-nm violet light? (b) What is the maximum kinetic energy of electrons ejected from calcium by 420 nm violet light, given that the binding energy…

Physics21.3 The Dual Nature of Light

ExemploElectron and Photon Momentum Compared(a) Calculate the momentum of a visible photon that has a wavelength of 500 nm. (b) Find the velocity of an electron having the same momentum. (c) What is the energy of the electron, and how does it compare with the…

Physics22.1 The Structure of the Atom

ExemploA hydrogen atom is struck by a photon. How much energy must be absorbed from the photon to raise the electron of the hydrogen atom from its ground state to its second orbital?
ExemploCharacteristic X-Ray EnergyCalculate the approximate energy of an X-ray emitted for an n = 2 to n = 1 transition in a tungsten anode in an X-ray tube.
ExemploWhat wavelength of light is emitted by an electron dropping from the third orbital to the ground state of a hydrogen atom?

Physics22.2 Nuclear Forces and Radioactivity

ExemploCreating a Decay EquationWrite the complete decay equation in Z^A X N notation for beta decay producing ^(137) Ba. Refer to the periodic table for values of Z.
ExemploAlpha Decay Energy Found from Nuclear MassesFind the energy emitted in the α decay of 239Pu.

Physics22.3 Half Life and Radiometric Dating

ExemploCarbon-11 DecayCarbon-11 has a half-life of 20.334 min. (a) What is the decay constant for carbon-11? If 1 kg of carbon-11 sample exists at the beginning of an hour, (b) how much material will remain at the end of the hour and (c)…
ExemploHow Old is the Shroud of Turin?Calculate the age of the Shroud of Turin given that the amount of ^(14) C found in it is 92 percent of that in living tissue.

Physics22.4 Nuclear Fission and Fusion

ExemploCalculating Energy from a Kilogram of Fissionable FuelCalculate the amount of energy produced by the fission of 1.00 kg of ^(235) U, given the average fission reaction of ^(235) U produces 200 MeV. 22.66

College Physics28.1 Einstein’s Postulates

ChecagemExplain how special relativity differs from general relativity.

College Physics28.2 Simultaneity And Time Dilation

Exemplo 28.1Calculating Δt for a Relativistic Event: How Long Does a Speedy Muon Live?Suppose a cosmic ray colliding with a nucleus in the Earth’s upper atmosphere produces a muon that has a velocity v=0.950c. The muon then travels at constant velocity and lives 1.52μs as measured in the muon’s frame…Com figura
Checagem1. What is γ if v=0.650c? 2. A particle travels at 1.90×10^8 m/s and lives 2.10×10^(−8) s when at rest relative to an observer. How long does the particle live as viewed in the laboratory?

College Physics28.3 Length Contraction

Exemplo 28.2Calculating Length Contraction: The Distance between Stars Contracts when You Travel at High VelocitySuppose an astronaut, such as the twin discussed in Simultaneity and Time Dilation, travels so fast that γ=30.00. (a) She travels from the Earth to the nearest star system, Alpha Centauri, 4.300 light years (ly) away…Com figura
ChecagemA particle is traveling through the Earth’s atmosphere at a speed of 0.750c. To an Earth-bound observer, the distance it travels is 2.50 km. How far does the particle travel in the particle’s frame of reference?

College Physics28.4 Relativistic Addition of Velocities

Exemplo 28.3Showing that the Speed of Light towards an Observer is Constant (in a Vacuum): The Speed of Light is the Speed of LightSuppose a spaceship heading directly towards the Earth at half the speed of light sends a signal to us on a laser-produced beam of light. Given that the light leaves the ship at speed c as observed from the ship,…Com figura
Exemplo 28.4Comparing the Speed of Light towards and away from an Observer: Relativistic Package DeliverySuppose the spaceship in the previous example is approaching the Earth at half the speed of light and shoots a canister at a speed of 0.750c. (a) At what velocity will an Earth-bound observer see the canister if it…Com figura
Exemplo 28.5Calculating a Doppler Shift: Radio Waves from a Receding GalaxySuppose a galaxy is moving away from the Earth at a speed 0.825 c. It emits radio waves with a wavelength of 0.525m. What wavelength would we detect on the Earth?
ChecagemSuppose a space probe moves away from the Earth at a speed 0. 350 c. It sends a radio wave message back to the Earth at a frequency of 1.50 GHz. At what frequency is the message received on the Earth?

College Physics28.5 Relativistic Momentum

ChecagemWhat is the momentum of an electron traveling at a speed 0.985c? The rest mass of the electron is 9.11×10^(−31) kg.

College Physics28.6 Relativistic Energy

Exemplo 28.6Calculating Rest Energy: Rest Energy is Very LargeCalculate the rest energy of a 1.00-g mass.
Exemplo 28.7Calculating Rest Mass: A Small Mass Increase due to Energy InputA car battery is rated to be able to move 600 ampere-hours (A·h) of charge at 12.0 V. (a) Calculate the increase in rest mass of such a battery when it is taken from being fully depleted to being fully charged. (b)…
Exemplo 28.8Comparing Kinetic Energy: Relativistic Energy Versus Classical Kinetic EnergyAn electron has a velocity v=0.990c. (a) Calculate the kinetic energy in MeV of the electron. (b) Compare this with the classical value for kinetic energy at this velocity. (The mass of an electron is 9.11×10^(−31) kg.)
ChecagemA photon decays into an electron-positron pair. What is the kinetic energy of the electron if its speed is 0.992c?

College Physics29.2 The Photoelectric Effect

Exemplo 29.1Calculating Photon Energy and the Photoelectric Effect: A Violet Light(a) What is the energy in joules and electron volts of a photon of 420-nm violet light? (b) What is the maximum kinetic energy of electrons ejected from calcium by 420-nm violet light, given that the binding energy…

College Physics29.3 Photon Energies and the Electromagnetic Spectrum

Exemplo 29.2X-ray Photon Energy and X-ray Tube VoltageFind the maximum energy in eV of an x-ray photon produced by electrons accelerated through a potential difference of 50.0 kV in a CRT like the one in Figure 29.13.
Exemplo 29.3Photon Energy and Effects for UVShort-wavelength UV is sometimes called vacuum UV, because it is strongly absorbed by air and must be studied in a vacuum. Calculate the photon energy in eV for 100-nm vacuum UV, and estimate the number of molecules…
Exemplo 29.4How Many Photons per Second Does a Typical Light Bulb Produce?Assuming that 10.0% of a 100-W light bulb’s energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, calculate the number of visible photons emitted per second.

College Physics29.4 Photon Momentum

Exemplo 29.6Photon Energy and MomentumShow that p=E/c for the photon considered in the Example 29.5.

College Physics29.6 The Wave Nature of Matter

Exemplo 29.7Electron Wavelength versus Velocity and EnergyFor an electron having a de Broglie wavelength of 0.167 nm (appropriate for interacting with crystal lattice structures that are about this size): (a) Calculate the electron’s velocity, assuming it is…

College Physics29.7 Probability: The Heisenberg Uncertainty Principle

Exemplo 29.8Heisenberg Uncertainty Principle in Position and Momentum for an Atom(a) If the position of an electron in an atom is measured to an accuracy of 0.0100 nm, what is the electron’s uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV?
Exemplo 29.9Heisenberg Uncertainty Principle for Energy and Time for an AtomAn atom in an excited state temporarily stores energy. If the lifetime of this excited state is measured to be 1.0×10^(−10)s, what is the minimum uncertainty in the energy of the state in eV?

College Physics29.8 The Particle-Wave Duality Reviewed

Exemplo 29.10Recoil of a Dust Particle after Absorbing a PhotonThe following topics are involved in this integrated concepts worked example: Photons (quantum mechanics) Linear Momentum Table 29.2 Topics A 550-nm photon (visible light) is absorbed by a 1.00-μg particle of dust in…

College Physics30.3 Bohr’s Theory of the Hydrogen Atom

Exemplo 30.1Calculating Wave Interference of a Hydrogen LineWhat is the distance between the slits of a grating that produces a first-order maximum for the second Balmer line at an angle of 15º?

College Physics30.4 X Rays: Atomic Origins and Applications

Exemplo 30.2Characteristic X-Ray EnergyCalculate the approximate energy of a Kα x ray from a tungsten anode in an x-ray tube.

College Physics30.8 Quantum Numbers and Rules

Exemplo 30.3What Are the Allowed Directions?Calculate the angles that the angular momentum vector L can make with the z-axis for l=1, as illustrated in Figure 30.54.

College Physics30.9 The Pauli Exclusion Principle

Exemplo 30.4How Many Electrons Can Be in This Shell?List all the possible sets of quantum numbers for the n=2 shell, and determine the number of electrons that can be in the shell and each of its subshells.
Exemplo 30.5Subshells and Totals for n=3How many subshells are in the n=3 shell? Identify each subshell, calculate the maximum number of electrons that will fit into each, and verify that the total is 2n^2.

College Physics31.3 Substructure of the Nucleus

Exemplo 31.1How Small and Dense Is a Nucleus?(a) Find the radius of an iron-56 nucleus. (b) Find its approximate density in kg/m^3, approximating the mass of ^(56)Fe to be 56 u.

College Physics31.4 Nuclear Decay and Conservation Laws

Exemplo 31.3β− Decay Energy from MassesFind the energy emitted in the β^− decay of ^(60)Co.

College Physics31.5 Half-Life and Activity

Exemplo 31.4How Old Is the Shroud of Turin?Calculate the age of the Shroud of Turin given that the amount of ^(14)C found in it is 92% of that in living tissue.
Exemplo 31.5How Great Is the 14C Activity in Living Tissue?Calculate the activity due to ^(14)C in 1.00 kg of carbon found in a living organism. Express the activity in units of Bq and Ci.
Exemplo 31.6What Mass of 137Cs Escaped Chernobyl?It is estimated that the Chernobyl disaster released 6.0 MCi of ^(137)Cs into the environment. Calculate the mass of ^(137)Cs released.

College Physics31.6 Binding Energy

Exemplo 31.7What Is BE/A for an Alpha Particle?Calculate the binding energy per nucleon of ^4He, the α particle.

College Physics32.2 Biological Effects of Ionizing Radiation

Exemplo 32.1Dose from Inhaled PlutoniumCalculate the dose in rem/y for the lungs of a weapons plant employee who inhales and retains an activity of 1.00 μCi of ^(239)Pu in an accident. The mass of affected lung tissue is 2.00 kg, the plutonium decays by…

College Physics32.5 Fusion

Exemplo 32.2Calculating Energy and Power from Fusion(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture. (b) If this takes place…

College Physics32.6 Fission

Exemplo 32.3Calculating Energy Released by FissionCalculate the energy released in the following spontaneous fission reaction: ^(238) U → ^(95) Sr + ^(140) Xe + 3n 32.26 given the atomic masses to be m(^(238)U)= 238.050784 u, m(^(95)Sr)= 94.919388 u, m(^(140)Xe)=…
Exemplo 32.4Calculating Energy from a Kilogram of Fissionable FuelCalculate the amount of energy produced by the fission of 1.00 kg of ^(235) U, given the average fission reaction of ^(235) U produces 200 MeV.

College Physics33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited

Exemplo 33.1Calculating the Mass of a PionTaking the range of the strong nuclear force to be about 1 fermi (10^(−15)m), calculate the approximate mass of the pion carrying the force, assuming it moves at nearly the speed of light.

College Physics33.3 Accelerators Create Matter from Energy

Exemplo 33.2Calculating the Voltage Needed by the Accelerator Between Accelerating TubesA linear accelerator designed to produce a beam of 800-MeV protons has 2000 accelerating tubes. What average voltage must be applied between tubes (such as in the gaps in Figure 33.9) to achieve the desired energy?

College Physics33.4 Particles, Patterns, and Conservation Laws

Exemplo 33.3Calculating Quantum Numbers in Two Decays(a) The most common decay mode of the Ξ^− particle is Ξ^−→Λ^0+π^−. Using the quantum numbers in the table given above, show that strangeness changes by 1, baryon number and charge are conserved, and lepton family…

College Physics33.5 Quarks: Is That All There Is?

Exemplo 33.4Quantum Numbers From Quark CompositionVerify the quantum numbers given for the Ξ^0 particle in Table 33.2 by adding the quantum numbers for its quark composition as given in Table 33.4.