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physics
modern physics

Questions and Answers of Modern Physics

A long cart moves at relativistic speed v. Sand is dropped into the cart at a rate dm/dt = σ in the ground frame. Assume that you stand on the ground next to where the sand falls in, and you
A long cart moves at relativistic speed v. S and is dropped into the cart at a rate dm/dt = σ in the ground frame. Assume that you grab the front of the cart and pull on it to keep it moving at
(a) Two masses m are connected by a string of length ? and constant tension T. The masses are released simultaneously. They collide and stick together. What is the mass, M, of the resulting blob?(b)
A massless string with constant tension T has one end attached to a wall and the other end attached to a mass M. The initial length of the string is ? (see Figure). The mass is released. Halfway to
(a) What is the energy of the bucket, as a function of distance from the wall? What is its maximum value? What is the maximum value of the kinetic energy?(b) What is the momentum of the bucket, as a
(a) A massless string with constant tension T has one end attached to a wall and the other end attached to a mass m. The initial length of the string is ? (see Figure). The mass is released. How long
A plane flies at constant height h. What should its speed be so that an observer on the ground sees the plane’s clock tick at the same rate as a ground clock? (Assume v << c.)
A clock starts on the ground and then moves up a tower at constant speed v. It sits on top of the tower for a time T and then descends at constant speed v. If the tower has height h, how long should
Person B moves at speed v (with v
A and B move at speed v (v
A rocket with proper length L accelerates from rest, with proper acceleration g (where gLwhere the last term is the standard special-relativistic ??head-start?? result. Derive the above relation by
A rocket starts at rest relative to a planet, a distance ? away. It accelerates toward the planet with proper acceleration g. Let ? and t be the readings on the rocket's and planet's clocks,
You stand at rest relative to a rocket that has synchronized clocks at its ends. It is then arranged for you and the rocket to move with relative speed v. A reasonable question to now ask is: As
Clock A sits at rest on the earth, and clock B circles the earth in an orbit that skims along the ground. Both A and B are essentially at the same radius, so the GR time-dilation effect yields no
A spaceship travels at speed v (v
(a) Answer the previous problem, except now let the spaceship turn around by moving in a small semicircle while maintaining speed v.(b) Answer the previous problem, except now let the spaceship turn
(a) In the first scenario in Section 13.5, calculate the ratio of B’s elapsed time to A’s, in terms of v0 and g. Assume that v0
Is there such a thing as a perfectly rigid body?
Moving clocks run slow. Does this result have anything to do with the time it takes light to travel from the clock to your eye?
Does the special-relativistic time dilation depend on the acceleration of the moving clock?
Someone says, “A stick that is length-contracted isn’t really shorter, it just looks shorter.” Do you agree?
Consider a stick that moves in the direction in which it points. Does its length contraction depend on whether this direction is across your vision or directly away from you?
In relativity, the order of two events in one frame may be reversed in another frame. Does this imply that there exists a frame in which I get off a bus before I get on it?
You are in a spaceship sailing along in outer space. Is there any way you can measure your speed without looking outside?
If you move at the speed of light, what shape does the universe take in your frame?
Two objects fly toward you, one from the east with speed u, and the other from the west with speed v. Is it correct that their relative speed, as measured by you, is u + v? Or should you use the
Two clocks at the ends of a train are synchronized with respect to the train. If the train moves past you, which clock shows the higher time?
A train moves at speed 4c/5. A clock is thrown from the back of the train to the front. As measured in the ground frame, the time of flight is 1 second. Is the following reasoning correct? “The
Person A chases person B. As measured in the ground frame, they have speeds 4c/5 and 3c/5, respectively. If they start a distance L apart (as measured in the ground frame), how much time will it take
Is the “the speed of light is the same in all inertial frames” postulate really necessary? That is, is it not already implied by the “the laws of physics are the same in all inertial frames”?
Imagine closing a very large pair of scissors. It is quite possible for the point of intersection of the blades to move faster than the speed of light. Does this violate anything in relativity?
Two twins travel away from each other at relativistic speed. The time-dilation result from relativity says that each twin sees the other’s clock running slow, so each says the other has aged less.
The momentum of an object with mass m and speed v is p = γmv. “A photon has zero mass, so it should have zero momentum.” Correct or incorrect?
It is not necessary to postulate the impossibility of accelerating an object to speed c. It follows as a consequence of the relativistic form of energy. Explain.
Find the photon energy in joules and in electron volts for an electromagnetic wave of frequency(a) 100MHz in the FM radio band, and(b) 900 kHz in the AM radio band.
An 80-kW FM transmitter operates at a frequency of 101.1 MHZ. How many photons per second are emitted by the transmitter?
What are the frequencies of photons having the following energies?(a) 1eV,(b) 1keV,(c) 1MeV.
Find the photon energy for light of wavelength(a) 450 nm,(b) 550 nm,(c) 650 nm.
Find the photon energy if the wavelength is(a) 0.1 nm (about 1 atomic diameter), and(b) 1 fm (1 fm = 10-15 m, about 1 nuclear diameter).
The wavelength of light emitted by a 3-mW He-Ne laser is 632 nm. If the diameter of the laser beam is 1.0 mm, what is the density of photons in the beam?
The work function for tungsten is 4.58eV.(a) Find the threshold frequency and wavelength for the photoelectric effect.(b) Find the maximum kinetic energy of the electrons if the wavelength of the
When light of wavelength 300 nm is incident on potassium, the emitted electrons have maximum kinetic energy of 2.03eV.(a) What is the energy of an incident photon?(b) What is the work function for
The threshold wavelength for the photoelectric effect for silver is 262 nm.(a) Find the work function for silver.(b) Find the maximum kinetic energy of the electrons if the incident radiation has a
The work function for cesium is 1.9eV.(a) Find the threshold frequency and wavelength for the photoelectric effect. Find the maximum kinetic energy of the electrons if the wavelength of the incident
When a surface is illuminated with light of wavelength 512 nm, the maximum kinetic energy of the emitted electrons is 0.54eV. What is the maximum kinetic energy if the surface is illuminated with
Find the shift in wavelength of photons scattered at θ = 60o.
When photons are scattered by electrons in carbon, the shift in wavelength is 0.33 pm. Find the scattering angle.
The wavelength of Compton-scattered photons is measured at θ = 90o. If λ/λ is to be 1.5%, what should the wavelength of the incident photons be?
Compton used photons of wavelength 0.0711 nm.(a) What is the energy of these photons?(b) What is the wavelength of the photon scattered at θ = 180o?(c) What is the energy of the photon scattered at
For the photons used by Compton, find the momentum of the incident photon and that of the photon scattered at 180o, and use the conservation of momentum to find the momentum of the recoil electron in
An X-ray photon of wavelength 6 pm that collides with an electron is scattered by an angle of 90o.(a) What is the change in wavelength of the photon?(b) What is the kinetic energy of the scattered
How many head-on Compton scattering events are necessary to double the wavelength of a photon having initial wavelength 200 pm?
Use Equation 17-13 to calculate the de Broglie wavelength for an electron of kinetic energy (a) 2.5eV, (b) 250eV, (c) 2.5keV, and (d) 25keV.
An electron has a wavelength of 200 nm. Find(a) Its momentum,(b) Its kinetic energy.
Find the energy of an electron in electron volts if its de Broglie wavelength is(a) 5 nm,(b) 0.01 nm.
A neutron in a reactor has kinetic energy of about 0.02 eV. Calculate the de Broglie wavelength of this neutron from Equation 17-12, where mc2 = 940 MeV is the rest energy of the neutron.
Use Equation 17-12 to find the de Broglie wavelength of a proton (rest energy mc2 = 938 MeV) that has a kinetic energy of 2 MeV.
A proton is moving at v = 0.003c, where c is the speed of light. Find its de Broglie wavelength.
Find the de Broglie wavelength of a baseball of mass 0.145 kg moving at 30 m/s.
An electron microscope uses electrons of energy 70keV. Find the wavelength of these electrons.
What is the de Broglie wavelength of a neutron with speed 106 m/s?
Suppose you have a spherical object of mass 4 g moving at 100 m/s. What size aperture is necessary for the object to show diffraction? Show that no common objects would be small enough to squeeze
A neutron has a kinetic energy of 10MeV. What size object is necessary to observe neutron diffraction effects? Is there anything in nature of this size that could serve as a target to demonstrate the
What is the de Broglie wavelength of an electron of kinetic energy 200eV? What are some common targets that could demonstrate the wave nature of such an electron?
Sketch the wave function y(x) and the probability distribution y 2(x) for the state n = 4 of a particle in a box.
(a) Find the energy of the ground state (n = 1) and the first two excited states of a proton in a one-dimensional box of length L = 10-15 m = 1 fm. (These are the order of magnitude of nuclear
(a) Find the energy of the ground state (n = 1) and the first two excited states of a proton in a one-dimensional box of length 0.2 nm (about the diameter of a H2 molecule). Calculate the wavelength
(a) Find the energy of the ground state and the first two excited states of a small particle of mass 1 mg confined to a one-dimensional box of length 1 cm.(b) If the particle moves with a speed of 1
A particle is in the ground state of a box of length L. Find the probability of finding the particle in the interval ∆x = 0.002L at(a) x = L/2,(b) x = 2L/3,(c) x = L. (Since ∆x is very small, you
Do Problem 48 for a particle in the first excited state (n = 2).
Do Problem 48 for a particle in the second excited state (n = 3).
The classical probability distribution function for a particle in a box of length L is given by P(x) = 1/L. Use this to find (x) and (x2)for a classical particle in such a box.
(a) Find (x) for the first excited state (n = 2) for a particle in a box of length L, and(b) Find (x2).
(a) Find (x) for the second excited state (n = 3) for a particle in a box of length L, and(b) Find (x2).
A particle in a one-dimensional box is in the first excited state (n = 2).(a) Sketch Ψ2(x) versus x for this state.(b) What is the expectation value (x) for this state?(c) What is the probability of
A particle of mass m has a wave function given by Ψ(x) = Ae-|x/a, where A and a are constants.(a) Find the normalization constant A.(b) Calculate the probability of finding the particle in the
A particle in a one-dimensional box of length L is in its ground state. Calculate the probability that the particle will be found in the region(a) 0 < x < L,(b) 0 < x < L,(c) 0 < x
Repeat Problem 56 for a particle in the first excited state of the box.
(a) For the wave functions corresponding to a particle in the nth state of a one-dimensional box of length L, show that (b) Compare this result for n >> 1 with your answer for the classical
The wave functions for a particle of mass m in a one-dimensional box of length L centered at the origin (so that the ends are at x = ?L/2) are given by Calculate and for the ground state.
Calculate and for the first excited state of the box described in Problem 59.
Explain why the maximum kinetic energy of electrons emitted in the photoelectric effect does not depend on the intensity of the incident light, but the total number of electrons emitted does.
It was once believed that if two identical experiments are done on identical systems under the same conditions, the results must be identical. Explain why this is not true, and how it can be modified
A light beam of wavelength 400 nm has an intensity of 100 W/m2.(a) What is the energy of each photon in the beam?(b) How much energy strikes an area of 1 cm2 perpendicular to the beam in 1 s?(c) How
A mass of 10-6 g is moving with a speed of about 10-1 cm/s in a box of length 1 cm. Treating this as a one-dimensional particle in a box, calculate the approximate value of the quantum number n.
(a) For the classical particle of Problem 67, find ∆x and ∆p, assuming that these uncertainties are given by ∆x/L = 0.01% and ∆p/p = 0.01%.(b) What is (∆x ∆p)/?
In 1987, a laser at Los Alamos National Laboratory produced a flash that lasted 1 x 10-12 s and had a power of 5.0 x 1015 W. Estimate the number of emitted photons if their wavelength was 400 nm.
You can’t see anything smaller than the wavelength λ used. What is the minimum energy of an electron needed in an electron microscope to see an atom, which has a diameter of about 0.1 nm?
A common flea that has a mass of 0.008 g can jump vertically as high as 20 cm. Estimate the de Broglie wavelength for the flea immediately after takeoff.
The work function for sodium is f = 2.3 eV. Find the minimum de Broglie wavelength for the electrons emitted by a sodium cathode illuminated by violet light with a wavelength of 420 nm.
Suppose that a 100-W source radiates light of wavelength 600 nm uniformly in all directions and that the eye can detect this light if only 20 photons per second enter a dark-adapted eye having a
Data for maximum kinetic energy of the electrons versus wavelength for the photoelectric effect using sodium are Plot these data so as to obtain a straight line and from your plot find (a) The work
The diameter of the pupil of the eye under room-light conditions is about 5 mm. (It can vary from about 1 to 8 mm.) Find the intensity of light of wavelength 600 nm such that 1 photon per second
A light bulb radiates 90 W uniformly in all directions.(a) Find the intensity at a distance of 1.5 m.(b) If the wavelength is 650 nm, find the number of photons per second that strike a surface of
When light of wavelength λ1 is incident on the cathode of a photoelectric tube, the maximum kinetic energy of the emitted electrons is 1.8 eV. If the wavelength is reduced to λ1/2, the maximum
A photon of energy E is scattered at an angle of ?. Show that the energy E' of the scattered photon is given by
A particle is confined to a one-dimensional box. In making a transition from the state n to the state n – 1, radiation of 114.8 nm is emitted; in the transition from the state n – 1 to the state
A particle confined to a one-dimensional box has a ground-state energy of 0.4 eV. When irradiated with light of 206.7 nm it makes a transition to an excited state. When decaying from this excited
When a surface is illuminated with light of wavelength l the maximum kinetic energy of the emitted electrons is 1.2 eV. If the wavelength λ = 0.8λ is used the maximum kinetic energy increases to
A simple pendulum of length 1 m has a bob of mass 0.3 kg. The energy of this oscillator is quantized to the values En = (n + 1/2)hf0, where n is an integer and fs is the frequency of the pendulum.(a)

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