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physics
modern physics

Questions and Answers of Modern Physics

A 0.100-µg speck of dust is accelerated from rest to a speed of 0.900c by a constant 1.00 x 106 N force. (a) If the non-relativistic form of Newton's second law (ΣF = mal is used, how far
After being produced in a collision between elementary particles, a positive pion ('π +) must travel down a 1.20-km-Iong tube to reach an experimental area. A ' π + particle has an average
A cube of metal with sides of length a sits at rest in a frame S with one edge parallel to the x-axis Therefore, in S the cube has volume a'. Frame S' moves along the x-axis with a speed u. As
The starships of the Solar Federation are marked with the symbol of the federation, a circle, while starships of the Denebian Empire are marked with the empire's symbol, an ellipse whose major axis
A space probe is sent to the vicinity of the star Capella, which is 42.2 light-years from the earth. (A light-year is the distance light travels in a year.) The probe travels with a speed of 0.9910c.
A particle is said to be extremely relativistic when its kinetic energy is much greater than its rest energy. (a) What is the speed of a particle (expressed as a fraction of c) such that the total
Everyday Time Dilation two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of 250m/s and then returns to New
Everyday Time Dilation two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of 250m/s and then returns to New
A nuclear bomb containing 8.00 kg of plutonium explodes. The sum of the rest masses of the products of the explosion is less than the original rest mass by one part in 104.(a) How much energy is
Cerenkov radiation the Russian physicist P A Cerenkov discovered that a charged particle traveling in a solid with a speed exceeding the speed of light in that material radiates electromagnetic
A photon with energy E is emitted by an atom with mass m. which recoils in the opposite direction. (a) Assuming that the motion of the atom can be treated non-relativistically, compute the recoil
In an experiment, two protons are shot directly toward each other, each moving at half the speed of light relative to the laboratory. (a) What speed does one proton measure for the other proton?(b)
For the protons in Problem 37 .59, suppose that their speed is such that each proton measures a speed of half the speed of light for the other proton. (a) What does an observer in the laboratory
Frame S' has an x-component of velocity u relative to frame S, and at t = t' = 0 the two frames coincide (see Fig. 37.3). A light pulse with a spherical wave front is emitted at the origin of S' at
In certain radioactive beta decay processes, the beta particle (an electron) leaves the atomic nucleus with a speed of 99.95% the speed of light relative to the decaying nucleus. If this nucleus is
A particle with mass m accelerated from rest by a constant force F will, according to Newtonian mechanics, continue to accelerate without bound; that is, as t → ∞, v → ∞. Show
Two events are observed in a frame of reference S to occur at the same space point, the second occurring 1.80 s after the first. In a second frame S' moving relative to S, the second event is
Two events are observed in a frame of reference S to occur at the same space point, the second occurring 1.80 s after the first. In a second frame S' moving relative to S, the second event is
Albert in Wonderland Einstein and Lorentz, being avid tennis players, playa fast-paced game on a court where they stand 20.0 m from each other Being very skilled players, they play with-out a net The
One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is A = 656.3 nm, in the red portion of the electromagnetic spectrum. In the light emitted from a distant
Measuring Speed by Radar a baseball coach uses a radar device to measure the speed of an approaching pitched baseball. This device sends out electromagnetic waves with frequency to and then measures
Space Travel to the stars requires hundreds or thousands of years, even at the speed of light. Some people have suggested that we can get around this difficulty by accelerating the rocket (and its
A spaceship moving at constant speed u relative to us broadcasts a radio signal at constant frequency f0. As the spaceship approaches us, we receive a higher frequency f; after it has passed, we
The Pole and Bam Paradox suppose a very fast runner (v = 0.600c) holding a long, horizontal pole runs through a barn open at both ends. The length of the pole (in its rest frame) is 6.00 m, and the
The French physicist Armand Fizeau was the first to measure the speed of light accurately. He also found experimentally that the speed, relative to the lab frame, of light traveling in a tank of
Lorentz Transformation for Acceleration using a method analogous to the one in the text to find the Lorentz transformation formula for velocity, we can find the Lorentz transformation for
A Realistic Version of the Twin Paradox A rocket ship leaves the earth on January 1, 2100. Stella, one of a pair of twins born in the year 2015, pilots the rocket (reference frame S'); the other
Determining the Masses of Stars many of the stars in the sky are actually binary stars, in which two stars orbit about their common center of mass. If the orbital speeds of the stars are high enough,
Relativity and the Wave Equation(a) Consider the Galilean transformation along the x-direction: x' = x ?? vt and t' = t. In frame S the wave equation for electromagnetic waves in a vacuum is where E
(b) How does this calculated minimum kinetic energy compare with the total rest mass energy of the created kaons?
The graph in Figure 38.34 shows the stopping potential as a function of the frequency of the incident light falling on a metal surface,(a) Find the photoelectric work function for this metal.(b) What
Response of the Eye the human eye is most sensitive to green light of wavelength 505nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a
A photon of green light has a wavelength of 520nm. Find the photon's frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.
A laser used to weld detached retinas emits light with a wavelength of 652nm in pulses that are 20.0 ms in duration. The average power during each pulse is 0.600 W. (a) How much energy is in each
An excited nucleus emits a gamma-ray photon with an energy of 2.45MeV. (a) What is the photon frequency? (b) What is the photon wavelength? (c) How does the wavelength compare with a typical nuclear
The photoelectric threshold wavelength of a tungsten surface is 272 run. Calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency
A clean nickel surface is exposed to light of wavelength 235nm. What is the maximum speed of the photoelectrons emitted from this surface? Use Table 38.1.
What would the minimum work function for a metal have to be for visible light (400-700mn) to eject photoelectrons?
A 75-W light source consumes 75 W of electrical power. Assume all this energy goes into emitted light of wavelength 600nm. (a) Calculate the frequency of the emitted light. (b) How many photons per
In a photoelectric-effect experiment, the maximum kinetic energy of the ejected photoelectrons is measured for various wavelengths of the incident light. Figure 38.35 shows a graph of this maximum
(a) A proton is moving at a speed much slower than the speed of light. It has kinetic energy K1 and momentum P1. If the momentum of the proton is doubled, so P2 = 2p1 how is its new kinetic energy K2
The photoelectric work function of potassium is 2.3eV if light having a wavelength of 250 run falls on potassium, find(a) The stopping potential in volts; (b) The kinetic energy in electron volts of
When ultraviolet light with a wavelength of 254 run falls on a clean copper surface, the stopping potential necessary to stop emission of photoelectrons is 0.181 V. (a) What is the photoelectric
A photon has momentum of magnitude 8.24 x 10-28 kg • m/s. (a) What is the energy of this photon? Give your answer in joules and in electron volts. (b) What is the wavelength of this photon? In what
Use Ballmer’s formula to calculate (a) The wavelength, (b) The frequency, and (c) The photon energy for the Hy line of the Ballmer series for hydrogen.
Find the longest and shortest wavelengths in the Lyman and Paschen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?
(1). An atom initially in an energy level with E = -6.52eV absorbs a photon that has wavelength 860 nm. What is the internal energy of the atom after it absorbs the photon?(2). An atom initially
(a) An atom initially in an energy level with E = -6.52eV absorbs a photon that has wavelength 860 nm. What is the internal energy of the atom after it absorbs the photon? (b) An atom initially in an
In a set of experiments on a hypothetical one-electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground state (n = I), as shown in the energy level
A 4.78-MeV alpha particle from a 226Ra decay makes a head-on collision with a uranium nucleus. A uranium nucleus has 92 protons. (a) What is the distance of closest approach of the alpha particle to
A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in "head-on" to a particular lead nucleus and stops 6.50 x 10-14m away from the center of the nucleus.
A hydrogen atom is in a state with energy -1.51eV. In the Bohr model, what is the angular momentum of the electron in the atom, with respect to an axis at the nucleus?
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.
A triply ionized beryllium ion, Be 3+ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. (a) What is the
How many photons per second are emitted by a 7.50-mW CO2 laser that bas a wavelength of 10.6µm?
PRK Surgery Photorefractive keratectomy (PRK) is a laser-based surgical procedure that corrects near- and farsightedness by removing part on the lens of the eye to change its curvature and hence
A large number of neon atoms are in thermal equilibrium. What is the ratio of the number of atoms in a 58 state to the number in a 3p state at? (a) 300 K; (b) 600 K; (c) 1200 K? The energies of these
(a) Show that as n gets very large, the energy levels of the hydrogen atom get closer and closer together in energy. (b) Do the radii of these energy levels also get closer together?
(a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the n = 1,2 and 3 levels.(b) Calculate the orbital period in each of these levels. (c) The average lifetime of the
A hydrogen atom undergoes a transition from the n = 5 to the n = 2 state. (a) What are the energy and wavelength of the photon that is emitted? (b) If the angular momentum is conserved and if the
Figure 38.10 a shows the energy levels of the sodium atom. The two lowest excited levels are shown in columns labeled 2P3/2 and 2p1/2. Find the ratio of the number of atoms in a 2P3/2 state to the
Protons are accelerated from rest by a potential difference of 4.00 kV and strike a metal target. If a proton produces one photon on impact, what is the minimum wavelength of the resulting x rays?
(a) What is the minimum potential difference between the filament and the target of an x-ray tube if the tube is to produce x rays with a wavelength of 0.150 run? (b) What is the shortest wavelength
X Rays from Television Screens Accelerating voltages in cathode-ray-tube (CRT) TVs are about 25.0 kV. What are? (a) The highest frequency and (b) The shortest wavelength (in nm) of the x rays that
X rays are produced in a tube operating at 18.0kV. After emerging from the tube, x rays with the minimum wavelength produced strike a target and are Compton-scattered through an angle of 45.0°. (a)
X rays with initial wavelength 0.0665 nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?
A beam of x rays with wavelength 0.0500nm is Compton scattered by the electrons in a sample. At what angle from the incident beam should you look to find x rays with a wavelength of?(a) 0.0542nm; (b)
If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of 35.0° from its original direction, find (a) The change in the wavelength of this photon; (b) The
A photon scatters in the backward direction (6 = 180°) from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in
Complete the derivation of the Compton-scattering formula, Eq. (38.23), following the outline given in Eqs. (38.24) through (38.27)
Determine λm the wavelength at the peak of the Planck distribution, and the corresponding frequency f, at these temperatures: (a) 3.00 K; (b) 300 K; (c) 3000 K.
A 100-W incandescent light bulb bas a cylindrical tungsten filament 30.0cm long, 0.40 mm in diameter, and with an emissivity of 0.26. (a) What is the temperature of the filament? (b) For what
The shortest visible wavelength is about 400 run. What is the temperature of an ideal radiator whose spectral emittance peaks at this wavelength?
Radiation bas been detected from space that is characteristic of an ideal radiator at T = 2.728 K. (This radiation is a relic of the Big Bang at the beginning of the universe.) For this temperature,
Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one bas a surface temperature T and 3.0 times the diameter of the hotter star(a) What is
(a) Show that the maximum in the Planck distribution, Eq. (38.32), occurs at a wavelength Am given by Am = hc/4.965kT (Eq. 38.33). As discussed in the text, 4.965 is the root of Eq. (38.34).(b)
Sirius B. The brightest star in the sky is Sirius, the Dog Star. It is actually a binary system of two stars, the smaller one (Sirius B) being a white dwarf. Spectral analysis of Sirius B indicates
Show that for large values of A the Planck distribution, Eq. (38.32), agrees with the Rayleigh distribution, Eq. (38.31).
Blue Super giants a typical blue supergiant star (the type that explode and leave behind black holes) bas a surface temperature of 30,000 K and a visual luminosity 100,000 times that of our sun. Our
Exposing Photographic Film the light-sensitive compound on most photographic films is silver bromide, Ag Br. A film is "exposed" when the light energy absorbed dissociates this molecule into its
An atom with mass m emits a photon of wavelength A. (a) What is the recoil speed of the atom? (b) What is the kinetic energy K of the recoiling atom? (c) Find the ratio KIE, where E is the energy of
When a certain photoelectric surface is illuminated with light of different wavelengths, the following stopping potentials are observed:Plot the stopping potential on the vertical axis against the
(a) If the average frequency emitted by a 200-W light bulb is 5.00 x 1014 Hz, and 10.0% of the input power is emitted as visible light, approximately how many visible-light photons are emitted per
(a) The wavelength of light incident on a metal surface is reduced from λ1 to, λ2. (Both λ1 and λ2 are less than the threshold wavelength for the surface.) When the wavelength is
A 2.50-W beam of light of wavelength 124 nm falls on a metal surface. You observe that the maximum kinetic energy of the ejected electrons is 4.16eV. Assume that each photon in the beam ejects a
Removing Vascular Lesions a pulsed dye laser emits light of wavelength 585nm in 450-µs pulses. Because this wavelength is strongly absorbed by the hemoglobin in the blood, the method is especially
The photoelectric work functions for particular samples of certain metals are as follows: cesium, 2.1eV; copper, 4.7eV; potassium, 2.3eV; and zinc, 4.3eV. (a) What is the threshold wavelength for
The negative muon has a charge equal to that of an electron but a mass that is 207 times as great. Consider hydrogen like atom consisting of a proton and a muon. (a) What is the reduced mass of the
An incident x-ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of 1800 from its initial direction. The wavelength of the
An incident x-ray photon of wavelength 0.0900nm is scattered in the backward direction from a free electron that is initially at rest. (a) What is the magnitude of the momentum of the scattered
(b) Show from Bohr's angular momentum result and Newton's law of gravitation that the radius of an earth-satellite orbit is directly proportional to the square of the quantum number, r = kn2 , where
(a) What is the smallest amount of energy in electron volts that must be given to a hydrogen atom initially in its ground level so that it can emit the If" line in the Ballmer series? (b) How many
A large number of hydrogen atoms are in thermal equilibrium. Let n2/n1, be the ratio of the number of atoms in an n = 2 excited state to the number of atoms in an n = 1 ground state. At what
A sample of hydrogen atoms is irradiated with light with wavelength 8S.5 nm, and electrons are observed leaving the gas.(a) If each hydrogen atom were initially in its ground level, what would be the
Light from an ideal spherical blackbody 15.0 cm in diameter is analyzed using a diffraction grating having 3850 lines/cm. When you shine this light through the grating, you observe that the
The Red Giant Betelgeuse The red giant Betelgeuse has a surface temperature of 3000 K and is 600 times the diameter of our sun. (If our sun were that large, we would be inside it!) Assume that it
An ideal spherical blackbody 24.0 cm in diameter is maintained at 225oC by an internal electrical heater and is immersed in a very large open-faced tank of water that is kept boiling by the energy
What must be the temperature of an ideal blackbody so that photons of its radiated light having the peak-intensity wavelength can excite the electron in the Bohr-model hydrogen atom from the ground
What must be the temperature of an ideal blackbody so that photons of its radiated light having the peak-intensity wavelength can excite the electron in the Bohr-model hydrogen atom from the ground
(b) Evaluate the correction for a hydrogen atom in which an electron in the nth level returns to the ground level. How does the answer depend on n?

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