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physics
modern physics

Questions and Answers of Modern Physics

Radium is a radioactive element whose nucleus emits an
Review Conceptual Example 9 for background pertinent to this problem. Suppose that the speed of light in a vacuum were one million times smaller than its actual value, so that c = 3.00 × 102 m/s.
Suppose that one gallon of gasoline produces 1.1 × 108 J of energy, and this energy is sufficient to operate a car for twenty miles. An aspirin tablet has a mass of 325 mg. If the aspirin could be
Two kilograms of water are changed(a) From ice at 0 °C into liquid water at 0 °C(b) From liquid water at 100 °C into steam at 100 °C. For each situation, determine the change in mass of the water.
Multiple-Concept Example 6 reviews the principles that play a role in this problem. A nuclear power reactor generates 3.0 × 109 W of power. In one year, what is the change in the mass of the nuclear
Multiple-Concept Example 6 explores the approach taken in problems such as this one. Quasars are believed to be the nuclei of galaxies in the early stages of their formation. Suppose that a quasar
An electron is accelerated from rest through a potential diff erence that has a magnitude of 2.40 × 107 V. The mass of the electron is 9.11 × 10-31 kg, and the negative charge of the electron has a
An object has a total energy of 5.0 × 1015 J and a kinetic energy of 2.0 × 1015 J. What is the magnitude of the object's relativistic momentum?
You are driving down a two-lane country road, and a truck in the opposite lane is traveling toward you. Suppose that the speed of light in a vacuum is c = 65 m/s. Determine the speed of the truck
Spaceships of the future may be powered by ion-propulsion engines in which ions are ejected from the back of the ship to drive it forward. In one such engine the ions are to be ejected with a speed
The spaceship Enterprise 1 is moving directly away from earth at a velocity that an earth-based observer measures to be +0.65c. A sister ship, Enterprise 2, is ahead of Enterprise 1 and is also
A person on earth notices a rocket approaching from the right at a speed of 0.75c and another rocket approaching from the left at 0.65c. What is the relative speed between the two rockets, as
Suppose that you are traveling on board a spacecraft that is moving with respect to the earth at a speed of 0.975c. You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what
Two identical spaceships are under construction. The constructed length of each spaceship is 1.50 km. After being launched, spaceship A moves away from earth at a constant velocity (speed is 0.850c)
Two atomic particles approach each other in a head-on collision. Each particle has a mass of 2.16 × 10-25 kg. The speed of each particle is 2.10 × 108 m/s when measured by an observer standing in
An electron and a positron have masses of 9.11 × 10-31 kg. They collide and both vanish, with only electromagnetic radiation appearing after the collision. If each particle is moving at a speed of
The speed of an ion in a particle accelerator is doubled from 0.460c to 0.920c. The initial relativistic momentum of the ion is 5.08 × 10-17 kg ∙ m/s. Determine (a) The mass (b) The magnitude of
A Klingon spacecraft has a speed of 0.75c with respect to the earth. The Klingons measure 37.0 h for the time interval between two events on the earth. What value for the time interval would they
An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of 10.800c and a mass of 1.67
The table gives the total energy and the rest energy for three objects in terms of an energy increment
Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the
A 6.00-kg object oscillates back and forth at the end of a spring whose spring constant is 76.0 N/m. An observer is traveling at a speed of 1.90 × 108 m/s relative to the fixed end of the spring.
Imagine playing golf in a world where the speed of light is only c = 3.40 m/s. Golfer A drives a ball down a fl at horizontal fairway for a distance that he measures as 75.0 m. Golfer B, riding in a
The rest energy E0 and the total energy E of three particles, expressed in terms of a basic amount of energy E′ = 5.98 × 10-10 J, are listed in the table. The speeds of these particles are large,
A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 12 years have elapsed on earth, and 9.2 years have elapsed on board the ship. How
As observed on earth, a certain type of bacterium is known to double in number every 24.0 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture
Suppose the straight-line distance between New York and San Francisco is 4.1 × 106 m (neglecting the curvature of the earth). A UFO is flying between these two cities at a speed of 0.70c relative to
Two particles, A and B, have the same mass, but particle A has a charge of +q and B has a charge of +2q. The particles are accelerated from rest through the same potential difference. Which one has
Suppose that the momentum of an electron is measured with complete accuracy (i.e., the uncertainty in its momentum is zero). The uncertainty in a simultaneous measurement of the electron's position
Photons are generated by a microwave oven in a kitchen and by an X-ray machine at a dentist's office. Which type of photon has the greater frequency, the greater energy, and the greater wavelength?
A laser emits a beam of light whose photons all have the same frequency. When the beam strikes the surface of a metal, photoelectrons are ejected from the surface. What happens if the laser emits
The surface of a metal plate is illuminated with light of a certain frequency. Which of the following conditions determine whether or not photoelectrons are ejected from the metal?1. The number of
The dissociation energy of a molecule is the energy required to break the molecule apart into its separate atoms. The dissociation energy for the cyanogen molecule is 1.22 Ã— 10-18 J.
A proton is located at a distance of 0.420 m from a point charge of+8.30 µC. The repulsive electric force moves the proton until it is at a distance of 1.58 m from the charge. Suppose that the
When light with a wavelength of 221 nm is incident on a certain metal surface, electrons are ejected with a maximum kinetic energy of 3.28 × 10-19 J. Determine the wavelength (in nm) of light that
A glass plate has a mass of 0.50 kg and a specific heat capacity of 840 J/(kg ∙ C°). The wavelength of infrared light is 6.0 × 10-5 m, while the wavelength of blue light is 4.7 × 10-7 m. Find
(a) How many photons (wavelength = 620 nm) must be absorbed to melt a 2.0-kg block of ice at 0 °C into water at 0 °C? (b) On the average, how many H2O molecules does one photon convert from the ice
A light source emits a beam of photons, each of which has a momentum of 2.3 Ã— 10-29 kg ? m/s. (a) What is the frequency of the photons? (b) To what region of the electromagnetic spectrum
A photon of red light (wavelength = 720 nm) and a Ping-Pong ball (mass = 2.2 × 10-3 kg) have the same momentum. At what speed is the ball moving?
A sample is bombarded by incident X-rays, and free electrons in the sample scatter some of the X-rays at an angle of θ = 122.08 with respect to the incident X-rays (see Figure 29.10). The scattered
An incident X-ray photon of wavelength 0.2750 nm is scattered from an electron that is initially at rest. The photon is scattered at an angle of θ = 180.0° in Figure 29.10 and has a wavelength of
An AM radio station broadcasts an electromagnetic wave with a frequency of 665 kHz, whereas an FM station broadcasts an electromagnetic wave with a frequency of 91.9 MHz. How many AM photons are
In the Compton effect, momentum conservation applies, so the total momentum of the photon and the electron is the same before and after the scattering occurs. Suppose that in Figure 29.10 the
Figure 29.10 shows the setup for measuring the Compton effect. With a fixed incident wavelength, a wavelength of λ′1 is measured for a scattering angle of λ′1 = 30.0°, whereas a wavelength of
A photon of wavelength 0.45000 nm strikes a free electron that is initially at rest. The photon is scattered straight backward. What is the speed of the recoil electron after the collision?
An X-ray photon is scattered at an angle of θ = 180.0° from an electron that is initially at rest. After scattering, the electron has a speed of 4.67 × 106 m/s. Find the wavelength of the incident
A bacterium (mass = 2 × 10-15kg) in the blood is moving at 0.33 m/s. What is the de Broglie wavelength of this bacterium?
What are (a) the wavelength of a 5.0-eV photon and (b) the de Broglie wavelength of a 5.0-eV electron?
An electron and a proton have the same speed. Ignore relativistic effects and determine the ratio λelectron/ λproton of their de Broglie wavelengths.
Recall from Section 14.3 that the average kinetic energy of an atom in a monatomic ideal gas is given by K̅E̅ = 3/2 kT, where k = 1.38 × 10-23 J/K and T is the Kelvin temperature of the gas.
In a Young's double-slit experiment that uses electrons, the angle that locates the first-order bright fringes is θA = 1.6 × 10-4 degrees when the magnitude of the electron momentum is pA = 1.2 ×
From a cliff that is 9.5 m above a lake, a young woman (mass = 41 kg) jumps from rest, straight down into the water. At the instant she strikes the water, what is her de Broglie wavelength?
The width of the central bright fringe in a diffraction pattern on a screen is identical when either electrons or red light (vacuum wavelength = 661 nm) pass through a single slit. The distance
Particle A is at rest, and particle B collides head-on with it. The collision is completely inelastic, so the two particles stick together after the collision and move off with a common velocity. The
The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 5.0% of the speed of light. Find the ratio of the photon wavelength to the de Broglie wavelength of the
A proton is confined to a nucleus that has a diameter of 5.5 × 10-15 m. If this distance is considered to be the uncertainty in the position of the proton, what is the minimum uncertainty in its
Light is shining perpendicularly on the surface of the earth with an intensity of 680 W/m2. Assuming that all the photons in the light have the same wavelength (in vacuum) of 730 nm, determine the
Particles pass through a single slit of width 0.200 mm (see Figure 29.14). The de Broglie wavelength of each particle is 633 nm. After the particles pass through the slit, they spread out over a
The minimum uncertainty Î”y in the position y of a particle is equal to its de Broglie wavelength. Determine the minimum uncertainty in the speed of the particle, where this minimum
A subatomic particle created in an experiment exists in a certain state for a time of Δt = 7.4 × 10-20 s before decaying into other particles. Apply both the Heisenberg uncertainty principle and
The interatomic spacing in a crystal of table salt is 0.282 nm. This crystal is being studied in a neutron diffraction experiment, similar to the one that produced the photograph in Figure 29.12a.
Two sources produce electromagnetic waves. Source B produces a wavelength that is three times the wavelength produced by source A. Each photon from source A has an energy of 2.1 × 10-18 J. What is
Find the de Broglie wavelength of an electron with a speed of 0.88c. Take relativistic effects into account.
The work function of a metal surface is 4.80 × 10-19J. The maximum speed of the electrons emitted from the surface is vA = 7.30 × 105 m/s when the wavelength of the light is λA. However, a maximum
How fast does a proton have to be moving in order to have the same de Broglie wavelength as an electron that is moving with a speed of 4.50 × 106 m/s?
In a television picture tube the electrons are accelerated from rest through a potential difference V. Just before an electron strikes the screen, its de Broglie wavelength is 0.900 × 10-11 m. What
Multiple-Concept Example 3 reviews the concepts necessary to solve this problem. Light is incident on the surface of metallic sodium, whose work function is 2.3 eV. The maximum speed of the
Some scientists have suggested that spacecraft with sails of the kind described in Conceptual Example 4 could be propelled by lasers. Suppose that such a sail is constructed of a highly reflective
Sunlight, whose visible wavelengths range from 380 to 750 nm, is incident on a sodium surface. The work function for sodium is W0 = 2.28 eV. Concepts: (i) Will electrons with a greater value of KEmax
An electron and a proton have the same kinetic energy and are moving at speeds much less than the speed of light. Concepts: (i) How is the de Broglie wavelength l related to the magnitude p of the
The maximum wavelength that an electromagnetic wave can have and still eject electrons from a metal surface is 485 nm. What is the work function W0 of this metal? Express your answer in electron
Radiation of a certain wavelength causes electrons with a maximum kinetic energy of 0.68 eV to be ejected from a metal whose work function is 2.75 eV. What will be the maximum kinetic energy (in eV)
Multiple-Concept Example 3 reviews the concepts necessary to solve this problem. Radiation with a wavelength of 238 nm shines on a metal surface and ejects electrons that have a maximum speed of 3.75
Consider applying the Bohr model to a neutral helium atom. The model takes into account a number of factors. Which one of the following does it not take into account? (a) The quantization of the
Consider the 5f and 6h subshells in a multiple-electron atom. Which of these subshells can contain 19 electrons? (a) Only the 6h subshell (b) Only the 5f subshell (c) Both subshells (d) Neither
Silver (Z = 47), copper (Z = 29), and platinum (Z = 78) can be used as the target in an X-ray tube. Rank in descending order (largest first) the energies needed for impinging electrons to knock a
The voltage applied across an X-ray tube is doubled. What happens to the cutoff wavelength in the spectrum of wavelengths emitted by the tube's metal target? (a) It also doubles. (b) It decreases
According to the Bohr model, what determines the shortest wavelength in a given series of wavelengths emitted by the atom? (a) The quantum number ni that identifies the higher energy level from
According to quantum mechanics, only one of the following combinations of the principal quantum number n and the orbital quantum number, is possible for the electron in a hydrogen atom. Which
The electron in a hydrogen atom is in the first excited state, when the electron acquires an additional 2.86 eV of energy. What is the quantum number n of the state into which the electron moves?
a) What is the ionization energy of a hydrogen atom that is in the n = 4 excited state? (b) For a hydrogen atom, determine the ratio of the ionization energy for the n = 4 excited state to the
A hydrogen atom is in the ground state. It absorbs energy and makes a transition to the n = 3 excited state. The atom returns to the ground state by emitting two photons. What are their wavelengths?
In the hydrogen atom, what is the total energy (in electron volts) of an electron that is in an orbit that has a radius of 4.761 x 10-10 m?
Consider the Bohr energy expression (Equation 30.13) as it applies to singly ionized helium He+ (Z = 2) and doubly ionized lithium Li2+ (Z = 3). This expression predicts equal electron energies for
A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we
A hydrogen atom emits a photon that has momentum with a magnitude of 5.452 x 10-27 kg ? m/s. This photon is emitted because the electron in the atom falls from a higher energy level into the n = 1
The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.0 x 10-15 m. The single electron in a hydrogen atom normally orbits the nucleus at a distance of 5.3 x 10-11 m. What
Doubly ionized lithium Li2+ (Z = 3) and triply ionized beryllium Be3+ (Z = 4) each emit a line spectrum. For a certain series of lines in the lithium spectrum, the shortest wavelength is 40.5 nm. For
(a) Derive an expression for the speed of the electron in the nth Bohr orbit, in terms of Z, n, and the constants k, e, and h. For the hydrogen atom, determine the speed in (b) The n = 1 orbit and
In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. Determine the angular speed of the electron, in revolutions per second, when it is in (a) The ground state
A hydrogen atom is in its second excited state. Determine, according to quantum mechanics, (a) The total energy (in eV) of the atom, (b) The magnitude of the maximum angular momentum the electron
The table lists quantum numbers for five states of the hydrogen atom. Which (if any) of them are not possible? For those that are not possible, explain why.
The orbital quantum number for the electron in a hydrogen atom is l = 5. What is the smallest possible value (the most negative) for the total energy of this electron? Give your answer in electron
It is known that the possible values for the magnetic quantum number m, are -4, -3, -2, -1, 0, +1, +2, +3, and +4. Determine the orbital quantum number l and the smallest possible value of the
The electron in a certain hydrogen atom has an angular momentum of 8.948 x 10-34 J.s. What is the largest possible magnitude for the z component of the angular momentum of this electron? For
Review Conceptual Example 1 and use the information therein as an aid in working this problem. Suppose that you're building a scale model of the hydrogen atom, and the nucleus is represented by a
An electron is in the n = 5 state. What is the smallest possible value for the angle between the z component of the orbital angular momentum and the orbital angular momentum?
Following the style used earlier, determine the electronic configuration of the ground state for yttrium Y (Z = 39).
Figure was constructed using the Pauli exclusion principle and indicates that the n = 1 shell holds 2 electrons, the n = 2 shell holds 8 electrons, and the n = 3 shell holds 18 electrons. These
Which of the following subshell configurations are not allowed? For those that are not allowed, give the reason why. (a) 3s1 (b) 2d2 (c) 3s4 (d) 4p8 (e) 5f12

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