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physics
modern physics

Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

Escape velocity from the Earth is 11.2 km/s. What would be the percent decrease in length of a 68.2-m-long spacecraft traveling at that speed as seen from Earth?
An unstable particle produced in an accelerator experiment travels at constant velocity, covering 1.00 m in 3.40 ns in the lab frame before changing ("decaying") into other particles. In the rest frame of the particle, determine (a) How long it lived before decaying, (b) How far it moved before
What is the momentum of a proton traveling at v = 068c?
(a) A particle travels at v = 0.15c. By what percentage will a calculation of its momentum be wrong if you use the classical formula?(b) Repeat for v = 0.75c.
A particle of mass m travels at a speed v = 0.22c. At what speed will its momentum be doubled?
An unstable particle is at rest and suddenly decays into two fragments. No external forces act on the particle or its fragments. One of the fragments has a speed of 0.60c and a mass of 6.68 × 10-27 kg while the other has a mass of 1.67 × 10-27 kg. What is the speed of the less massive fragment?
A certain type of elementary particle travels at a speed of 2.70 × 108 m/s. At this speed, the average lifetime is measured to be 4.76 × 10-6s. What is the particle's lifetime at rest?
What is the percent change in momentum of a proton that accelerates from? (a) 0.45c to 0.85c, (b) 0.85c to 0.98c?
The total annual energy consumption in the United States is about 1 × 1020 J. How much mass would have to be converted to energy to fuel this need?
Calculate the mass of a proton (1.67 × 10-27 kg) in MeV/c2.
Calculate the kinetic energy and momentum of a proton traveling 2.90 × 108 m/s.
What is the momentum of a 950-MeV proton (that is, its kinetic energy is 950 MeV)?
What is the speed of an electron whose kinetic energy is 1.12 MeV?
(a) How much work is required to accelerate a proton from rest up to a speed of 0.985c? (b) What would be the momentum of this proton?
You travel to a star 135 light-years from Earth at a speed of 2.90 × 108 m/s. What do you measure this distance to be?
At what speed will an object's kinetic energy be 33% of its rest energy?
A proton is traveling in an accelerator with a speed of 1.0 × 108 m/s. By what factor does the proton's kinetic energy increase if its speed is doubled?
To accelerate a particle of mass m from rest to speed 0.90c requires work W1. To accelerate the particle from speed 0.90c to 0.99c requires work W2. Determine the ratio W2/W1.
Suppose there was a process by which two photons, each with momentum 0.65 MeV/c. could collide and make a single particle. What is the maximum mass that the particle could possess?
What is the speed of a proton accelerated by a potential difference of 165 MV?
The kinetic energy of a particle is 45 MeV. If the momentum is 121 MeV/c, what is the particle's mass?
Calculate the speed of a proton (m = 1.67 × 10-27 kg) whose kinetic energy is exactly half (a) Its total energy, (b) Its rest energy.
What is the speed of a pion if its average lifetime is measured to be 4.40 × 10-8 s? At rest, its average lifetime is 2.60 × 10-8s.
Calculate the kinetic energy and momentum of a Proton (m = 1.67 × 10-27 kg) traveling 8.65 × 107 m/s. By what percentages would your calculations have been in error if you had used classical formulas?
Suppose a spacecraft of mass 17,000 kg is accelerated to 0.15c. (a) How much kinetic energy would it have? (b) If you used the classical formula for kinetic energy, by what percentage would you be in error?
A negative muon traveling at 53% the speed of light collides head on with a positive muon traveling at 65% the speed of light. The two muons (each of mass 105.7MeV/c2) annihilate, and produce how much electromagnetic energy?
Two identical particles of mass m approach each other at equal and opposite speeds, v. The collision is completely inelastic and results in a single particle at rest. What is the mass of the new particle? How much energy was lost in the collision? How much kinetic energy was lost in this collision?
Show that the kinetic energy KE of a particle of mass m is related to its momentum p by the equation p = √KE2 + 2KE mc2/c.
A person on a rocket traveling at 0.40c (with respect to the Earth) observes a meteor come from behind and pass her at a speed she measures as 0.40c. How fast is the meteor moving with respect to the Earth?
Two spaceships leave Earth in opposite directions, each with a speed of 0.60c with respect to Earth.(a) What is the velocity of spaceship 1 relative to spaceship 2?(b) What is the velocity of spaceship 2 relative to spaceship 1?
A spaceship leaves Earth traveling at 0.65c. A second spaceship leaves the first at a speed of 0.82c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired(a) In the same direction the first spaceship is already moving,(b) Directly backward toward
In an Earth reference frame, a star is 49 light-years away. How fast would you have to travel so that to you the distance would be only 35 light-years?
A spaceship in distress sends out two escape pods in opposite directions. One travels at a speed v1 = +0.7c in one direction, and the other travels at a speed v2 = - 0.80c in the other direction, as observed from the spaceship. What speed does the first escape pod measure for the second escape pod?
Rocket A passes Earth at a speed of 0.65c. At the same time, rocket B passes Earth moving 0.95c relative to Earth in the same direction as A. How fast is B moving relative to A when it passes A?
Your spaceship, traveling at 0.90c, needs to launch a probe out the forward hatch so that its speed relative to the planet that you are approaching is 0.95c. With what speed must it leave your ship?
What is the speed of a particle when its kinetic energy equals its rest energy? Does the mass of the particle affect the result?
The nearest star to Earth is Proxima Centauri, 4.3 lightyears away. (a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.9 years, as measured by travelers on the spacecraft? (b) How long does the trip take according to Earth observers?
According to the special theory of relativity, the factor γ that determines the length contraction and the time dilation is given by γ = 1/√1 - v2/c2. Determine the numerical values of γ for an object moving at speed v = 0.01c, 0.05c, 0.10c, 0.20c, 0.30c, 0.40c, 0.50c, 0.60c, 0.70c, 0.80c,
At what speed v will the length of a 1.00-m stick look 10.0% shorter (90.0 cm)?
How many grams of matter would have to be totally destroyed to run a 75-W lightbulb for 1.0 year?
An electron (m = 9.11 × 10-31 kg) is accelerated from rest to speed v by a conservative force. In this process, its potential energy decreases by 6.20 × 10-14 J. Determine the electron's speed, v.
Show analytically that a particle with momentum p and energy E has a speed given by
Two protons, each having a speed of 0.990c in the laboratory, are moving toward each other. Determine(a) The momentum of each proton in the laboratory,(b) The total momentum of the two protons in the laboratory, and(c) The momentum of one proton as seen by the other proton.
When two moles of hydrogen molecules (H2) and one mole of oxygen molecules (O2) react to form two moles of water (H2O), the energy released is 484 kJ. How much does the mass decrease in this reaction? What % of the total original mass is this?
Make a graph of the kinetic energy versus momentum for(a) A particle of nonzero mass,(b) A particle with zero mass.
At what speed do the relativistic formulas for (a) Length (b) Time intervals differ from classical values by 1.00%? (This is a reasonable way to estimate when to use relativistic calculations rather than classical.)
In a nuclear reaction two identical particles are created, traveling in opposite directions. If the speed of each particle is 0.82c, relative to the laboratory frame of reference, what is one particle's speed relative to the other particle?
A 36,000-kg spaceship is to travel to the vicinity of a star 6.6 light-years from Earth. Passengers on the ship want the (one-way) trip to take no more than 1.0 year. How much work must be done on the spaceship to bring it to the speed necessary for this trip?
Suppose a 14,500-kg spaceship left Earth at a speed of 0.90c. What is the spaceship's kinetic energy? Compare with the total U.S. annual energy consumption (about 1020 J).
A pi meson of mass mπ decays at rest into a muon (mass mμ) and a neutrino of negligible or zero mass. Show that the kinetic energy of the muon is KEμ = (mπ - mμ)2 c2 / (2 mπ).
An astronaut on a spaceship traveling at 0.75c relative to Earth measures his ship to be 23 m long. On the ship, he eats his lunch in 28 min. (a) What length is the spaceship according to observers on Earth? (b) How long does the astronaut's lunch take to eat according to observers on Earth?
An electron is accelerated so that its kinetic energy is greater than its rest energy mc2 by a factor of (a) 5.00, (b) 999. What is the speed of the electron in each case?
You are traveling in a spaceship at a speed of 0.70c away from Earth. You send a laser beam toward the Earth traveling at velocity c relative to you. What do observers on the Earth measure for the speed of the laser beam?
A farm boy studying physics believes that he can fit a 13.0-m-long pole into a 10.0-m-long barn if he runs fast enough, carrying the pole. Can he do it? Explain in detail. How does this fit with the idea that when he is running the barn looks even shorter than 10.0 m?
You decide to travel to a star 62 light-years from Earth at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip?
An atomic clock is taken to the North Pole, while another stays at the Equator. How far will they be out of synchronization after 2.0 years has elapsed?
An airplane travels 1300 km/h around the Earth in a circle of radius essentially equal to that of the Earth, returning to the same place. Using special relativity, estimate the difference in time to make the trip as seen by Earth and by airplane observers.
A friend speeds by you in her spacecraft at a speed of 0.720c. It is measured in your frame to be 4.80 m long and 1.35 m high.(a) What will be its length and height at rest?(b) How many seconds elapsed on your friend's watch when 20.0 s passed on yours?(c) How fast did you appear to be traveling
Determine about how fast Mr Tompkins is traveling in the Chapter-Opening Photograph. Do you agree with the picture in terms of the way Mr Tompkins would see the world? Explain.
Examine the experiment of Fig. 26-5 from O1`s reference frame. In this case, O1 will be at rest and will see the lightning bolt at B1 and B2, before the lightning bolt at A1 and A2 Will O1 recognize that O2, who is moving with speed v to the left, will see the two events as simultaneous? Explain in
Using Example 26-2 as a guide, show that for objects that move slowly in comparison to c, the length contraction formula is roughly ℓ ≈ ℓ0(1 - ½ v2/c2). Use this approximation to find the "length shortening" ∆ℓ = ℓ0 - ℓ of the train in Example 26-6 if the train travels at 100 km/h
In Example 26-5, the spaceship is moving at 0.90c in the horizontal direction relative to an observer on the Earth. If instead the spaceship moved at 0.90c directed at above the horizontal, what would be the painting's dimensions as seen by the observer on Earth?
Protons from outer space crash into the Earth's atmosphere at a high rate. These protons create particles that eventually decay into other particles called muons. This cosmic debris travels through the atmosphere. Every second, dozens of muons pass through your body. If a muon is created 30 km
As a rough rule, anything traveling faster than about 0.1c is called relativistic-that is, special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom (radius 0.53 × 10-10 m) and state whether or not it is relativistic. (Treat the electron as though it were in
An electron and a proton are accelerated through the same voltage. Which has the longer wavelength? Explain why.
(a) List at least three successes of the Bohr model of the atom, according to Section 27-12. (b) List at least two observations that the Bohr model could not explain, according to Section 27-13.
State if a continuous or a line spectrum is produced by each of the following: (a) A hot solid object; (b) An excited, rarefied gas; (c) A hot liquid; (d) Light from a hot solid that passes through a cooler rarefied gas; (e) A hot dense gas. For each, if a line spectrum is produced, is it an
1. Which of the following statements is true regarding how blackbody radiation changes as the temperature of the radiating object increases? (a) Both the maximum intensity and the peak wavelength increase. (b) The maximum intensity increases, and the peak wavelength decreases. (c) Both the maximum
In Rutherford's famous set of experiments described in Section 27-10, the fact that some alpha particles were deflected at large angles indicated that (choose all that apply) (a) The nucleus was positive. (b) Charge was quantized. (c) The nucleus was concentrated in a small region of space. (d)
1. Which of the following electron transitions between two energy states (n) in the hydrogen atom corresponds to the emission of a photon with the longest wavelength?(a) 2 → 5.(b) 5 → 2.(c) 5 → 8.(d) 8 → 5.2. If we set the potential energy of an electron and a proton to be zero when they
1. Which of the following is the currently accepted model of the atom? (a) The plum-pudding model. (b) The Rutherford atom. (c) The Bohr atom. (d) None of the above. 2. Light has all of the following except: (a) Mass. (b) Momentum. (c) Kinetic energy. (d) Frequency. (e) Wavelength.
1. Which of the following is necessarily true? (a) Red light has more energy than violet light. (b) Violet light has more energy than red light. (c) A single photon of red light has more energy than a single photon of violet light. (d) A single photon of violet light has more energy than a single
1. Which of the following can be thought of as either a wave or a particle? (a) Light. (b) An electron. (c) A proton. (d) All of the above. 2. When you throw a baseball, its de Broglie wavelength is (a) The same size as the ball. (b) About the same size as an atom. (c) About the same size as an
What is the value of e/m for a particle that moves in a circle of radius 14 mm in a 0.86-T magnetic field if a perpendicular electric field will make the path straight?
What is the energy of photons (joules) emitted by a 91.7-MHz FM radio station?
A typical gamma ray emitted from a nucleus during radioactive decay may have an energy of 320 keV. What is its wavelength? Would we expect significant diffraction of this type of light when it passes through an everyday opening, such as a door?
Calculate the momentum of a photon of yellow light of Wavelength 5.80 × 10-7 m.
What is the momentum of a λ = 0.014 nm X-ray photon?
What minimum frequency of light is needed to eject electrons from a metal whose work function is 4.8 × 10-19 J?
What is the longest wavelength of light that will emit electrons from a metal whose work function is 2.90 eV?
(a) What is the velocity of a beam of electrons that go undeflected when passing through crossed (perpendicular) electric and magnetic fields of magnitude 1.88 × 104 V/m and 2.60 × 10-3 T, respectively? (b) What is the radius of the electron orbit if the electric field is turned off?
The work functions for sodium, cesium, copper, and iron are 2.3, 2.1, 4.7, and 4.5 eV, respectively. Which of these metals will not emit electrons when visible light shines on it?
In a photoelectric-effect experiment it is observed that no current flows unless the wavelength is less than 550 nm. (a) What is the work function of this material? (b) What stopping voltage is required if light of wavelength 400 nm is used?
Barium has a work function of 2.48 eV. What is the maximum kinetic energy of electrons if the metal is illuminated by UV light of wavelength 365 nm? What is their speed?
When UV light of wavelength 255 nm falls on a metal surface, the maximum kinetic energy of emitted electrons is 1.40 eV. What is the work function of the metal?
The threshold wavelength for emission of electrons from a given surface is 340 nm. What will be the maximum kinetic energy of ejected electrons when the wavelength is changed to(a) 280 nm,(b) 360 nm?
Show that the energy E (in electron volts) of a photon whose wavelength is (nm) is given byUse at least 4 significant figures for values of h, c, e (see inside front cover).
An oil drop whose mass is 2.8 Ã— 10-15 kg is held at rest between two large plates separated by 1.0 cm (Fig. 27-3), when the potential difference between the plates is 340 V. How many excess electrons does this drop have?
A high-frequency photon is scattered off of an electron and experiences a change of wavelength of 1.7 × 10-4 nm. At what angle must a detector be placed to detect the scattered photon (relative to the direction of the incoming photon)?
The quantity h/mc, which has the dimensions of length, is called the Compton wavelength. Determine the Compton wavelength for (a) An electron, (b) A proton. (c) Show that if a photon has wavelength equal to the Compton wavelength of a particle, the photon's energy is equal to the rest energy of
X-rays of wavelength λ = 0.140 nm are scattered from carbon. What is the expected Compton wavelength shift for photons detected at angles (relative to the incident beam) of exactly? (a) 45°, (b) 90°, (c) 180°?
How much total kinetic energy will an electron-positron pair have if produced by a 3.64-MeV photon?
What is the minimum photon energy needed to produce a μ+ μ- pair? The mass of each μ (muon) is 207 times the mass of an electron. What is the wavelength of such a photon?
A gamma-ray photon produces an electron and a positron, each with a kinetic energy of 285 keV. Determine the energy and wavelength of the photon.
Calculate the wavelength of a 0.21-kg ball traveling at 0.10 m/s.
What is the wavelength of a neutron (m = 1.67 × 10-27 kg) traveling at 8.5 × 104 m/s?
How hot is a metal being welded if it radiates most strongly at 520 nm?
Through how many volts of potential difference must an electron, initially at rest, be accelerated to achieve a wavelength of 0.27 nm?
An electron has a de Broglie wavelength λ = 4.5 × 10-10 m. (a) What is its momentum? (b) What is its speed? (c) What voltage was needed to accelerate it from rest to this speed?
Show that if an electron and a proton have the same nonrelativistic kinetic energy, the proton has the shorter wavelength.

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