Concepts of Modern. Physics. Sixth Edition. Arthur Beiser. Boston Burt Ridge, II, Dubuque, IA Instructor's Solution Manual for Fundamentals of Physics. Problem Solutions. 1. If the speed of light were smaller than it is, would relativistic phenomena presranretiper.cf Beiser – Modern Physics. Concepts of Modern. Physics. Sixth Edition. Arthur Beiser. Boston Burr Ridge, IL . It can have a variety of solutions, including complex ones.

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Here you can get it directly ⇩ ⇰ File formats: ePub, PDF, Kindle, audiobook, mobi, ZIP. Download >>Concepts of Modern Physics 6th Edition. Concepts of Modern Physics: Student Solution Manual by Arthur Beiser, , available at Book Depository with free delivery. pdf. solution manual of physics by arthur beiser. Pages An athlete has learned enough physics to know that if he measures from the earth a time interval .

Problem Solutions 1. If the speed of light were smaller than it is, would relativistic phenomena be more or less conspicuous than they are now? An athlete has learned enough physics to know that if he measures from the earth a time interval on a moving spacecraft, what he finds will be greater than what somebody on the spacecraft would measure. He therefore proposes to set a world record for the m dash by having his time taken by an observer on a moving spacecraft. Is this a good idea? Sol All else being the same, including the rates of the chemical reactions that govern our brains and bodies, relativisitic phenomena would be more conspicuous if the speed of light were smaller. If we could attain the absolute speeds obtainable to us in the universe as it is, but with the speed of light being smaller, we would be able to move at speeds that would correspond to larger fractions of the speed of light, and in such instances relativistic effects would be more conspicuous. Sol Even if the judges would allow it, the observers in the moving spaceship would measure a longer time, since they would see the runners being timed by clocks that appear to run slowly compared to the ship's clocks. Actually, when the effects of length contraction are included discussed in Section 1. Inha University Department of Physics 5. Two observers, A on earth and B in a spacecraft whose speed is 2. To B, does A's watch seem to run fast, run slow, or keep the same time as his own watch? In Equation 1. In this problem, the time t is the time that observer A measures as the time that B's clock takes to record a time change of t o s 00 1 0 3.

Optical spectra, however, depend upon the possible states of the outermost electrons, which, together with the transitions permitted for them, are different for atoms of different atomic number. The wavelength is In a triplet state, they are parallel Distinguish between singlet and triplet states in atoms with two outer electrons.

Inha University Department of Physics 1. The energy needed to detach the electron from a hydrogen atom is Why do you think the latter energy is greater? This means that the additional attractive force of the two protons exceeds the mutual repulsion of the electrons to increase the binding energy. At what temperature would the average kinetic energy of the molecules in a hydrogen sample be equal to their binding energy? When a molecule rotates, inertia causes its bonds to stretch.

This is why the earth bulges at the equator. What effects does this stretching have on the rotational spectrum of the molecule? In addition, the higher the quantum number J and hence the greater the angular momentum , the faster the rotation and the greater the distortion, so the spectral lines are no longer evenly spaced.

Quantitatively, the parameter I the moment of inertia of the molecule is a function of J, with I larger for higher J. Thus, all of the levels as given by Equation 8.

It should be noted that if I depends on J, the algebraic steps that lead to Equation 8. Find the mass number of the unknown carbon isotope. For the different isotopes, the atomic separation, which depends on the charges of the atoms, will be essentially the same.

The ratio of the moments of inertia will then be the ratio of the reduced masses. The rotational spectrum of HCI contains the following wavelengths: A least-squares fit from a spreadsheet program gives 0. From Equation 8. A Hg 35 Cl Molecule emits a 4. Find the interatomic distance in this molecule. This is an example of Bohr's correspondence principle. Show that a similar correspondence holds for a diatomic molecule rotating about its center of mass. The hydrogen isotope deuterium has an atomic mass approximately twice that of ordinary hydrogen.

Does H 2 or HD have the greater zero-point energy? How does this affect the binding energies of the two molecules? HD has the greater reduced mass, and hence the smaller frequency of vibration v o and the smaller zero- point energy.

HD is the more tightly bound, and has the greater binding energy since its zero-point energy contributes less energy to the splitting of the molecule. Plot the potential energy of this molecule versus internuclear distance in the vicinity of 0. The levels are shown below, where the vertical scale is in units of 10 J and the horizontal scale is in units of 10 m.

The lowest vibrational states of the 23 Na 35 Cl molecule are 0. Find the approximate force constant of this molecule. Solving Equation 8. Is it likely that an HCl molecule will be vibrating in its first excited vibrational state at room temperature? Atomic masses are given in the Appendix. It's important to note that in the above calculations, the symbol "k " has been used for both a spring constant and Boltzmann's constant, quantities that are not interchangeable.

Find the ratio between the numbers of atoms in each state in sodium vapor at l K. The moment of inertia of the H 2 molecule is 4. If so, at what temperature does this occur?

Find and v rms for an assembly of two molecules, one with a speed of 1. At what temperature will the average molecular kinetic energy in gaseous hydrogen equal the binding energy of a hydrogen atom?

Find the width due to the Doppler effect of the How many independent standing waves with wavelengths between 95 and How many with wavelengths between Similarly, the number of waves between A thermograph measures the rate at which each small portion of a persons skin emits infrared radiation. To verify that a small difference in skin temperature means a significant difference in radiation rate, find the percentage difference between the total radiation from skin at 34 o and at 35 o C.

At what rate would solar energy arrive at the earth if the solar surface had a temperature 10 percent lower than it is? Using 1. An object is at a temperature of o C. At what temperature would it radiate energy twice as fast? At what rate does radiation escape from a hole l0 cm 2 in area in the wall of a furnace whose interior is at o C? Find the surface area of a blackbody that radiates kW when its temperature is o C. If the blackbody is a sphere, what is its radius?

The brightest part of the spectrum of the star Sirius is located at a wavelength of about nm. What is the surface temperature of Sirius? A gas cloud in our galaxy emits radiation at a rate of 1. If the cloud is spherical and radiates like a blackbody, find its surface temperature and its diameter.

Find the specific heat at constant volume of 1. The median energy is that energy for which there are many occupied states below the median as there are above. The Fermi energy in silver is 5. This is the reason for the symmetry of the curves in Fig. The density of zinc is 7. The electronic structure of zinc is given in Table 7. Calculate the Fermi energy in zinc. Thus, there are two free electrons per atom. Are we justified in considering the electron energy distribution as continuous in a metal?

The number of states per electronvolt is and the distribution may certainly be considered to be continuous. To do this, use Eq 9. The Fermi-Dirac distribution function for the free electrons in a metal cannot be approximated by the Maxwell-Boltzmann function at STP for energies in the neighborhood of k T.

As calculated in Sec. Note that Eq. In this problem, the time t is the time that observer A measures as the time that B's clock takes to record a time change of to. For this problem. If one of the characteristic wavelengths of the light the galaxy emits is nm. A galaxy in the constellation Ursa Major is receding from the earth at The classical and relativistic frequencies. If the receiver on earth can measure frequencies to the nearest hertz.

For the classical effect. A spacecraft receding from the earth emits radio waves at a constant frequency of Hz. Inha University Department of Physics. The denominator will be indistinguishable from 1 at low speed. For an approaching source. For a receding source. If the angle between the direction of motion of a light source of frequency vo and the direction from it to an observer is 0. To an observer on the earth. A spacecraft antenna is at an angle of 10o relative to the axis of the spacecraft.

In the absence of forces. All definitions are arbitrary. A woman leaves the earth in a spacecraft that makes a round trip to the nearest star. Solving for v. If the CM of the box is to remain in its original place. The distance 5 is the product vt. A burst of electromagnetic radiation of energy Eo is emitted by one end of the box. According to classical physics. In its own frame of reference. Expanding the binomial. Algebraically and numerically.

An observer detects two explosions. An equally valid method. Another observer finds that the two explosions occur at the. Take the direction of the ship's motion assumed parallel to its axis to be the positive x-direction. In the unprimed frame. In the reference frame of the fixed stars. The relative velocities will have opposite directions.

Looking out of a porthole. The speed with which B is seen to approach A. A and B. A man on the moon sees two spacecraft. That is. KEmax is not proportional to the frequency. Chapter 2 Problem Solutions 1.

If Planck's constant were smaller than it is. If not. Light from the sun arrives at the earth. The total power is then. Using the result from part a.

K max.

To see the same result without using as much algebra. In this frame. The distance between adjacent atomic planes in calcite CaCO3 is 0.

At 45o from the beam direction the scattered x-rays have a wavelength of 2. To simplify the algebra somewhat. With this expression. This may be re-expressed as Inha University Department of Physics.

If the electron moves off at an angle of 40o with the original photon direction. Show that. The wavelength of each photon will be hc 1. As an alternative. At this point. E must be greater than 2mc2. Equation 2. What thickness of water would give the same shielding for such gamma rays as 10 mm of lead? The linear absorption coefficient for 1-MeV gamma rays in lead is 78 m By how much is the photon energy reduced in this situation if the ex. By how much is the photon energy reduced from 26 the full The mass of a 57 Fe atom is 9.

When a nucleus emits a photon. The square root must be expanded. E2 Inha University Department of Physics. It so happens that a relativistic treatment of the recoiling nucleus gives the same numerical result, but without intermediate approximations or solution of a quadratic equation.

Chapter 3. The atomic spacing in rock salt. This energy is much less than the neutron's rest energy. Problem Solutions keeping extra figures in the intermediate calculations. For a photon with the same energy. Note that the kinetic energy is very small compared to the electron rest energy. Problem Solutions Green light has a wavelength of about nm.

Show that if the total energy of a moving particle greatly exceeds its rest energy. In the above calculation.

Verify the statement in the text that. For those more comfortable with calculus. Express the wavelength x in terms of vg. For a kinetic energy of keV. Multiplying by mvg. The final result is. For a calculational shortcut. Solving for the width L. The uncertainty in position of each atom is therefore finite. The position of an ideal-gas molecule is not restricted.

The atoms in a solid possess a certain minimum zero-point energy even at 0 K. In such a situation. In the current problem. The number of waves in each group is the pulse duration divided by the wave period. Chapter 4. In this case. Equating these energies.

For a classical particle subject to an inverse-square attractive force such as two oppositely charged particles or two uniform spheres subject to gravitational attraction in a circular orbit. In the Bohr model. For the system to be bound. Sommerfeld's approach was on the wrong track. Because the magnetic behavior of a moving charge depends on its velocity. Combining to find v The most accurate November.

A close cheek of the units is worthwhile. Compare the uncertainty in the momentum of an electron confined to a region of linear dimension ao with the momentum of an electron in a ground-state Bohr orbit.

L mvR 6. The energy of the photon emitted is then -El. A proton and an electron. The energies are proportional to the reciprocals of the wavelengths. The fact that this mass change is too small to measure that is. As a result. In this situation. When an excited atom emits a photon. E in that problem. In the above. As in part a. As in Problem Note that in this form. Inserting numerical values. For a tritium atom. A mixture of ordinary hydrogen and tritium. In the approximation that the reduced masses are the same.

The scale is close. The emitted photon's wavelength is hc 1. To these nonpenetrating particles. The fraction scattered by less than 1 o is 1. Show that twice as many alpha particles are scattered by a foil through angles between 60o and 90o as are scattered through angles of 90o or more.

In special relativity. This suggests that we can treat a photon that passes near the sun in the same way as Rutherford treated an alpha particle that passes near a nucleus. In fact. Chapter 5 Problem Solutions 1. Of the many ways to find this integral.

Such a superposition would necessarily have a non. A linear superposition of such waves could give a normalizable wave function. As the potential energy increases with x.

The amplitude increases as the wavelength increases because a larger wavelength means a smaller momentum indicated as well by the lower kinetic energy. An important property of the eigenfunctions of a system is that they are orthogonal to one another.

To show orthogonality. To do the integrals directly. From either a table or repeated integration by parts. As shown in the text. This form makes evaluation of the definite integral a bit simpler. K Find the value of the normalization constant A. The minimum energy is then 2mL which is three times the ground-state energy of a particle in a one-dimensional box of length L.

None of the integers nx. The uncertainty principle dictates that such a particle would have an infinite uncertainty in momentum. A generalization of the above to any case where the potential energy is a symmetric function of x. The other two integrals may be found from tables. The first and third integrals are seen to be zero see Example 5. In both of the above integrals.

H is the maximum pendulum height. As a check on the last result. Show that a0 is a solution of Eq. The three quantum numbers needed to describe an atomic electron correspond to the variation in the radial direction. To show normalization. In evaluating the integral at the limits. It is possible to express the integral in terms of real and imaginary parts. Lz must be an integer multiple of. Under what circumstances.

In the quantum theory. Find the percentage difference between L and the maximum value of Lz for an atomic electron in p. Differentiating the above expression for P r with respect to r and setting the derivative equal to zero. How much more likely is the electron in a ground-state hydrogen atom to be at the distance ao from the nucleus than at the distance 2ao?

The ratio of the probabilities is then the ratio of the product r2 R10 r 2 evaluated at the different distances. Unsold's theorem states that for any value of the orbital quantum number l. Note that one term appears twice. The integrand is then an odd function of u when n and m are both even or both odd. To make use of symmetry arguments. If one of n or m is even and the other odd.

The terms involving sines vanish. The orbital radius is proportional to n2 See Equation 4. The nuclei of ordinary helium atoms, 4 He , contain two protons and two neutrons each; the nuclei of another type of helium 2 3 , contain two protons and one neutron each. The properties of liquid 4 atom, 2 He 2 He and liquid 3 2 He are different because one type of helium atom obeys the exclusion principle but the other does not.

In general, using the expression for the sum of the squares of the first n integers, the number of elements would be. The ionization energies of Li. This outer electron is then relatively hard to d etach. The outermost electron in each of these atoms is further from the nucleus for higher atomic number. The 3d subshell is empty. Li and Na. Why are Cl atoms more chemically active than Cl. In each of the following pairs of atoms. F and Cl. Na and Si. Li and F. If the total number of electrons were odd.

What must be true of the subshells of an atom which has a 1S0 ground state? This state has the lowest possible values of L and J.

From the law of cosines. Optical spectra. Explain why the x-ray spectra of elements of nearby atomic numbers are qualitatively very similar. The wavelength is hc 1. In a triplet state. Chapter 8 Problem Solutions 1. In addition. Denoting the unknown mass number by x and the ratio of the frequencies as r. When a molecule rotates. It should be noted that if I depends on J. For the different isotopes. A Hg35Cl Molecule emits a 4.

Does H2 or HD have the greater zero-point energy? HD has the greater reduced mass, and hence the smaller frequency of vibration vo and the smaller zero- point energy. The lowest vibrational states of the 23Na35Cl molecule are 0. An individual atom is not likely to he vibrating in its first ex cited level. It's important to note that in the above calculations. Chapter 9 Problem Solutions 1. If so. The moment of inertia of the H2 molecule is 4. Find v and vrms for an assembly of two molecules.

To verify that a small difference in skin temperature means a significant difference in radiation rate. Find the surface area of a blackbody that radiates kW when its temperature is oC.

An object is at a temperature of oC. At what rate does radiation escape from a hole l0 cm2 in area in the wall of a furnace whose interior is at oC? If the blackbody is a sphere. If the cloud is spherical and radiates like a blackbody. Solving for D. The radius of a sphere with this surface area is. In terms of temperature. Evaluating the integrals. The number of states per electronvolt is 3 9. Equation 9. To do this. For energies in the neighborhood of kT. The Fermi-Dirac distribution function for the free electrons in a metal cannot be approximated by the Maxwell-Boltzmann function at STP for energies in the neighborhood of kT.

Which is much greater than one. Flag for inappropriate content. Related titles. Mark W. Dittman-Heat and Thermodynamics 7th ed. Krane Kenneth S. Classical Electrodynamics 3rd Ed J. Jackson - Solutions - Pg. Introduction to Electrodynamics Solutions Manual - Griffiths. Jump to Page. Search inside document. Inha University Department of Physics Chapter 1. Inha University Department of Physics for the intermediate calculations.

Chapter 7 1. Problem Solutions A beam of electrons enters a uniform 1. Inha University Department of Physics 9. Inha University Department of Physics but not to the same extent as the filled shells. Rodrigo Leon. Anonymous b6H1rBG. Laurien Merindha. Qasim Ijaz Ahmed. AnNybell Chicaiza. Sma Shamsi. Konrad Nied. Miguel Ferreira. Muhammad Sajid.

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Linda Smith. Intan Sertufi. How fast must a spacecraft travel relative to the earth for each day on the spacecraft to correspond to 2 d on the earth? A certain particle has a lifetime of 1. How far does it go before decaying if its speed is 0.

If one of the characteristic wavelengths of the light the galaxy emits is nm, what is the corresponding wavelength measured by astronomers on the earth? For this problem, v 1. A spacecraft receding from the earth emits radio waves at a constant frequency of Hz. If the receiver on earth can measure frequencies to the nearest hertz, at what spacecraft speed can the difference between the relativistic and classical Doppler effects be detected?

For the classical effect, assume the earth is stationary.

Show that this formula includes Eqs. An astronaut whose height on the earth is exactly 6 ft is lying parallel to the axis of a spacecraft moving at 0. What is his height as measured by an observer in the same spacecraft? By an observer on the earth? From Equation 1. How much time does a meter stick moving at 0. The meter stick is parallel to its direction of motion. A spacecraft antenna is at an angle of 10o relative to the axis of the spacecraft. If the spacecraft moves away from the earth at a speed of 0.

To an observer on the earth, the length in the direction of the spacecraft's axis will be contracted as described by Equation 1. A woman leaves the earth in a spacecraft that makes a round trip to the nearest star, 4 light- years distant, at a speed of 0.

All definitions are arbitrary, but some are more useful than others. Dynamite liberates about 5. What fraction of its total energy content is this? At what speed does the kinetic energy of a particle equal its rest energy? An electron has a kinetic energy of 0. Find its speed according to classical and relativistic mechanics. A particle has a kinetic energy 20 times its rest energy. Find the speed of the particle in terms of c. How much work in MeV must be done to increase the speed of an electron from 1.

Figure 1. A burst of electromagnetic radiation of energy Eo is emitted by one end of the box.

If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other. In its own frame of reference, a proton takes 5 min to cross the Milky Way galaxy, which is about light-years in diameter. The result of Problem does not give an answer accurate to three significant figures. The value of the speed may be substituted into Equation 1. An observer detects two explosions, one that occurs near her at a certain time and another that occurs 2.

Another observer finds that the two explosions occur at the, same place. What time interval separates the explosions to the second observer? Inserting this into Equation 1.

An equally valid method, and a good cheek, is to note that when the relative speed of the observers 5. Algebraically and numerically, the different methods give the same result. Take the direction of the ship's motion assumed parallel to its axis to be the positive x-direction, so that in the frame of the fixed stars the unprimed frame , the signal arrives at an angle 0 with respect to the positive x-direction.

A man on the moon sees two spacecraft, A and B, coming toward him from opposite directions at the respective speeds of 0. For the speed with which he is approaching B? For the speed with which he is approaching A? The relative velocities will have opposite directions, but the relative speeds will be the same.

If Planck's constant were smaller than it is, would quantum phenomena be more or less conspicuous than they are now? That is, quantum phenomena would be less conspicuous than they are now. Find the energy of a nm photon. How many photons per second does it emit? Light from the sun arrives at the earth, an average of 1. Assume that sunlight is monochromatic with a frequency of 5. Using the result from part a , 4.

The maximum wavelength for photoelectric emission in tungsten is nm. What wavelength of light must be used in order for electrons with a maximum energy of 1. What is the maximum wavelength of light that will cause photoelectrons to be emitted from sodium? What will the maximum kinetic energy of the photoelectrons be if nm light falls on a sodium surface?

From Equation 2. A metal surface illuminated by 8. Show that it is impossible for a photon to give up all its energy and momentum to a free electron. This is the reason why the photoelectric effect can take place only when photons strike bound electrons. An easier alternative is to consider the interaction in the frame where the electron is at rest after absorbing the photon.

In this frame, the final energy is the rest energy of the electron, mec2, but before the interaction, the electron would have been moving to conserve momentum , and hence would have had more energy than after the interaction, and the photon would have had positive energy, so energy could not be conserved. Electrons are accelerated in television tubes through potential differences of about 10 kV. Find the highest frequency of the electromagnetic waves emitted when these electrons strike the screen of the tube.

What kind of waves are these? The distance between adjacent atomic planes in calcite CaCO3 is 0. Find the smallest angle of Bragg scattering for 0.

What is the frequency of an x-ray photon whose momentum is 1. In See. Show that this assumption is reasonable by calculating the Compton wavelength of a Na atom and comparing it with the typical x-ray wavelength of 0. A beam of x-rays is scattered by a target. At 45o from the beam direction the scattered x-rays have a wavelength of 2.

What is the wavelength of the x-rays in the direct beam? An x-ray photon of initial frequency 3. Find its new frequency. At what scattering angle will incident keV x-rays leave a target with an energy of 90 keV?

A photon whose energy equals the rest energy of the electron undergoes a Compton collision with an electron. If the electron moves off at an angle of 40o with the original photon direction, what is the energy of the scattered photon? Consider the expression for the recoil angle as given preceding the solution to Problem A positron collides head on with an electron and both are annihilated.

Each particle had a kinetic energy of 1. The wavelength of each photon will be hc 1. Show that, regardless of its initial energy, a photon cannot undergo Compton scattering through an angle of more than 60o and still be able to produce an electron-positron pair. Start by expressing the Compton wavelength of the electron in terms of the maximum photon wavelength needed for pair production.

The linear absorption coefficient for 1-MeV gamma rays in lead is 78 m The linear absorption coefficients for 2.

What thickness of water would give the same shielding for such gamma rays as 10 mm of lead? What thickness of copper is needed to reduce the intensity of the beam in Exercise 48 by half. The sun's mass is 2. Find the approximate gravitational red shift in light of wavelength nm emitted by the sun. As discussed in Chap. These photons constitute gamma rays. When a nucleus emits a photon, it recoils in the opposite direction.

The mass of a Fe atom is 9. By how much is the photon energy reduced from the full By how much is the photon energy reduced in this situation if the ex- cited Fe nucleus is part of a 1. Such a source was used in the experiment described in See. What is the original frequency and the change in frequency of a This approximation gives the previous result. Of course, a relativistic calculation is correct here, but it is interesting to see what a classical calculation produces.

That is, its total energy must be nonnegative. A photon and a particle have the same wavelength. Can anything be said about how their linear momenta compare? About how the photon's energy compares with the particle's total energy? Problem Solutions 3.

Find the de Broglie wavelength of a 1. By what percentage will a nonrelativistle calculation of the de Broglie wavelength of a keV electron be in error? Problem Solutions keeping extra figures in the intermediate calculations.

The atomic spacing in rock salt, NaCl, is 0. Find the kinetic energy in eV of a neutron with a de Broglie wavelength of 0. Is a relativistic calculation needed?

Such neutrons can be used to study crystal structure. This energy is much less than the neutron's rest energy, and so the nonrelativistic calculation is completely valid.

Problem Solutions 9. Green light has a wavelength of about nm. Through what potential difference must an electron be accelerated to have this wavelength? Note that the kinetic energy is very small compared to the electron rest energy, so the nonrelativistic calculation is valid. In the above calculation, multiplication of numerator and denominator by c2 and use of the product he in terms of electronvolts avoided further unit conversion. Show that if the total energy of a moving particle greatly exceeds its rest energy, its de Broglie wavelength is nearly the same as the wavelength of a photon with the same total energy.

Problem Solutions An electron and a proton have the same velocity Compare the wavelengths and the phase and group velocities of their de Broglie waves. From Equation 3.

Verify the statement in the text that, if the phase velocity is the same for all wavelengths of a certain wave phenomenon that is, there is no dispersion , the group and phase velocities are the same. Find the phase and group velocities of the de Broglie waves of an electron whose kinetic energy is keV.

Both will assume the validity of Equation 3. The final result is, or course, the same. What effect on the scattering angle in the Davisson-Germer experiment does increasing the electron energy have?

In Sec. Consider a beam of eV electrons directed at a nickel target. The potential energy of an electron that enters the target changes by 26 eV. Obtain an expression for the energy levels in MeV of a neutron confined to a one-dimensional box 1. What is the neutron's minimum energy? The diameter of an atomic nucleus is of this order of magnitude. A proton in a one-dimensional box has an energy of keV in its first excited state. How wide is the box?

Solving for the width L, h2 6. The atoms in a solid possess a certain minimum zero-point energy even at 0 K, while no such restriction holds for the molecules in an ideal gas. Use the uncertainty principle to explain these statements. The uncertainty in position of each atom is therefore finite, and its momentum and hence energy cannot be zero. The position of an ideal-gas molecule is not restricted, so the uncertainty in its position is effectively infinite and its momentum and hence energy can be zero.

The position and momentum of a 1. If its position is located to within 0. A marine radar operating at a frequency of MHz emits groups of electromagnetic waves 0. The time needed for the reflections of these groups to return indicates the distance to a target.

The number of waves in each group is the pulse duration divided by the wave period, which is the pulse duration multiplied by the frequency, 8. The great majority of alpha particles pass through gases and thin metal foils with no deflections. To what conclusion about atomic structure does this observation lead? Determine the distance of closest approach of 1. In this case, at the point of closest approach the proton will have no kinetic energy, and so the potential energy at closest approach will be the initial kinetic energy, taking the potential energy to be zero in the limit of very large separation.

What is the shortest wavelength present in the Brackett series of spectral lines?

In the Bohr model, the electron is in constant motion. How can such an electron have a negative amount of energy? For the system to be bound, the total energy, the sum of the positive kinetic energy and the total negative potential energy, must be negative. For a classical particle subject to an inverse-square attractive force such as two oppositely charged particles or two uniform spheres subject to gravitational attraction in a circular orbit, the potential energy is twice the negative of the kinetic energy.

This quantity got its name because it first appeared in a theory by the German physicist Arnold Sommerfeld that tried to explain the fine structure in spectral lines multiple lines close together instead of single lines by assuming that elliptical as well as circular orbits are possible in the Bohr model.

Find the quantum number that characterizes the earth's orbit around the sun. The earth's mass is 6. Compare the uncertainty in the momentum of an electron confined to a region of linear dimension ao with the momentum of an electron in a ground-state Bohr orbit. What effect would you expect the rapid random motion of the atoms of an excited gas to have on the spectral lines they produce? A proton and an electron, both at rest initially, combine to form a hydrogen atom in the ground state.

A single photon is emitted in this process. What is its wavelength? The energy of the photon emitted is then -El, and the wavelength is hc 1. In what part of the spectrum is this? A beam of electrons bombards a sample of hydrogen. Through what potential difference must the electrons have been accelerated if the first line of the Balmer series is to be emitted?

A potential difference of The longest wavelength in the Lyman series is Use the figures to find the longest wavelength of light that could ionize hydrogen. When an excited atom emits a photon, the linear momentum of the photon must be balanced by the recoil momentum of the atom.

As a result, some of the excitation energy of the atom goes into the kinetic energy of its recoil. Is the effect a major one? A nonrelativistic calculation is sufficient here. The fact that this mass change is too small to measure that is, the change is measured indirectly by measuring the energies of the emitted photons means that a nonrelativistic calculation should suffice. Equation 4.

In the above, the rest energy of the hydrogen atom is from the front endpapers. Find the wavelength of the photon emitted when the muonic atom drops to its ground state. In what part of the spectrum is this wavelength? A mixture of ordinary hydrogen and tritium, a hydrogen isotope whose nucleus is approximately 3 times more massive than ordinary hydrogen, is excited and its spectrum observed.

Find the wavelength of the photon emitted in this process if the electron is assumed to have had no kinetic energy when it combined with the nucleus. The scale is close, but not exact, and of course there are many more levels corresponding to higher n.

The emitted photon's wavelength is hc 1. A certain ruby laser emits 1. The Rutherford scattering formula fails to agree with the data at very small scattering angles. Can you think of a reason?