Arthur Beiser. Boston Burt Ridge, II, Dubuque, IA Madison, WI New York San Francisco St. Louis. Bangkok Bogotá Caracas Kuala Lumpur Lisbon London. Concepts of Modern. Physics. Sixth Edition. Arthur Beiser. Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis. Problem Solutions. 1. If the speed of light were smaller than it is, would relativistic phenomena sibacgamete.cf Beiser – Modern Physics.
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Berlin: K. Schnabel, [in German] Meinsma, K. Paris: Vrin, [in French] Melamed, S. Geld en vrijheid. Vertaald uit het Frans door Jelle Noorman. Il percorso da Spinoza a Maimonide. Immagine e funzione teorica di Spinoza negli scritti jenesi di Hegel.
L'immagine di Spinoza in Germania da Leibniz a Marx. Translated by Samuel Shirley. Filosofia e negazione di Dio da Spinoza a D'Holbach. Kallen Boston: G.
Nebst einem Abrisse der Schelling'schen und Hegel'schen Philosophie.
Aarau: H. Marx legge Spinoza. Paolo, Spinoza, Rosenzweig. Il carteggio Spinoza- Oldenburg — El racionalismo. Descartes y Espinosa. Berlin: R.
A cura di Enrico Opocher. Milano: A. Lessing's Stellung zur Philosophie des Spinoza. Autre chose et la mystique. Beck, [in German] Roelofsz, C. Zeist: J. Oxford: Clarendon, Roth, Leon: Spinoza. Ein psychologisch-philosophisches Antitheton. Bibliografia degli scritti italiani su Spinoza dal al Studi su Cartesio e Spinoza.
Translated from the German by Elizabeth S. Haldane and Frances H. London: K. Hamburg und Gotha: Fr. Edited and translated by Shlomo Avineri.
Mendelssohn und F.
Jacobi und der Gottesbegriff Spinozas. New York: W. Vertaald door Hans van Cuijlenborg. Vortrag gehalten im Vereine der Literaturfreunde zu Wien.
Wien: A. Siren İdemen. Translated by Miriam Ron and Jacky Feldman. Amsterdam: Wereldbibliotheek, [in Dutch] Klever, Wim: Mannen rond Spinoza — : Presentatie van een emanciperende generatie. Antieke bronnen van een moderne denker. Translated by Agnieszka Kolakowska et al. South Bend, IN: St. Berlin: Druck von W. Le concept de disposition chez Spinoza. Politique des dispositions. Stuttgart : W. Breslau : T. Ricostruzione filosofico-storica di un incontro impossibile.
Della potenza e le sue determinazioni. Edited by Warren Montag , translated by Ted Stolze. La storia della filosofia, la metafisica della durata e il ruolo di Spinoza. Entre Vermeer et Spinoza. Barcelona: Montesinos, [in Spanish] Matheron, Alexandre ed. Berlin: K. A single photon is emitted in this process. What is its wavelength? The energy of the photon emitted is then -E l , and the wavelength is nm, 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.
The energies are proportional to the reciprocals of the wavelengths, and so the wavelength of the photon needed to ionize hydrogen is nm. 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. As in Problem , a relativistic calculation is manageable; the result would be ,. 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.
The difference between the wavelengths would then be The values of R and RT are proportional to the respective reduced masses, and their ratio is. Inserting numerical values, nm.
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 nm. The Rutherford scattering formula fails to agree with the data at very small scattering angles. Can you think of a reason? To these nonpenetrating particles, the nucleus is either partially or completely screened by the atom's electron cloud, and the scattering analysis, based on a pointlike positively charged nucleus, is not applicable.
A certain ruby laser emits 1. What fraction of a beam of 7.
Through what angle will it be scattered? The scattering angle is then. Show that twice as many alpha particles are scattered by a foil through angles between 60 o and 90 o as are scattered through angles of 90 o or more.
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, with an attractive gravitational force replacing the repulsive electrical force.
Adapt Eq. The mass and radius of the sun are respectively 2. In fact, general relativity shows that this result is exactly half the actual deflection, a conclusion supported by observations made during solar clipses as mentioned in Sec. Which of the wave functions in Fig. Why not? Figure c has discontinuous derivative in the shown interval. Figure d is finite everywhere in the shown interval. Figure f is discontinuous in the shown interval. As mentioned in Sec. Equation 5. Does this wave function meet all the above requirements?
If not, could a linear superposition of such wave functions meet these requirements? What is the significance of such a superposition of wave functions? Inha University Department of Physics A linear superposition of such waves could give a normalizable wave function, corresponding to a real particle. One of the possible wave functions of a particle in the potential well of Fig. As the potential energy increases with x, the particle's kinetic energy must decrease, and so the wavelength increases.
The amplitude increases as the wavelength increases because a larger wavelength means a smaller momentum indicated as well by the lower kinetic energy , and the particle is more likely to be found where the momentum has a lower magnitude. From either a table or repeated integration by parts, the indefinite integral is.
A particle is in a cubic box with infinitely hard walls whose edges are L long Fig. Before substitution into Equation 5. A beam of electrons is incident on a barrier 6. Use Eq. What bearing would you think the uncertainty principle has on the existence of the zero-point energy of a harmonic oscillator?
The uncertainty principle dictates that such a particle would have an infinite uncertainty in momentum, and hence an infinite uncertainty in energy. This contradiction implies that the zero-point energy of a harmonic oscillator cannot be zero. The other two integrals may be found from tables, from symbolic-manipulation programs, or by any of the methods outlined at the end of this chapter or in Special Integrals for Harmonic Oscillators, preceding the solutions for Section 5.
The integrals are. A pendulum with a 1. The period of the pendulum is 1. Would you expect the zero-point oscillations to be detectable? What is the corresponding quantum number? Find the transmitted and reflected currents. The transmitted current is T 1. The three quantum numbers needed to describe an atomic electron correspond to the variation in the radial direction, the variation in the azimuthal direction the variation along the circumference of the classical orbit , and the variation with the polar direction variation along the direction from the classical axis of rotation.
Chapter 6 Problem Solutions 1. Why is it natural that three quantum numbers are needed to describe an atomic electron apart from electron spin? The improper definite integral in u is known to have the value 2 and so the given function is normalized.
In Exercise 12 of Chap. Inha University Department of Physics 7. Compare the angular momentum of a ground-state electron in the Bohr model of the hydrogen atom with its value in the quantum theory. Under what circumstances, if any, is L z equal to L? Find the percentage difference between L and the maximum value of L z for an atomic electron in p, d , and f states. Verify this. Differentiating the above expression for P r with respect to r and setting the derivative equal to zero,. Find the most probable value of r for a 3d electron in a hydrogen atom.
How much more likely is the electron in a ground-state hydrogen atom to be at the distance a o from the nucleus than at the distance 2a o? The ratio of the probabilities is then the ratio of the product r 2 R 10 r 2 evaluated at the different distances. The probability of finding an atomic electron whose radial wave function is R r outside a sphere of radius r o centered on the nucleus is a Calculate the probability of finding a 1s electron in a hydrogen atom at a distance greater than a o from the nucleus.
According to classical physics, the electron therefore cannot ever exceed the distance 2a o from the nucleus. With the help of the wave functions listed in Table 6. The terms involving sines vanish, with the result of. The integrand is then an odd function of u when n and m are both even or both odd, and hence the integral is zero. If one of n or m is even and the other odd, the integrand is an even function of u and the integral is nonzero.
Show that the magnetic moment of an electron in a Bohr orbit of radius r n is proportional to Find the minimum magnetic field needed for the Zeeman effect to be observed in a spectral line of nm wavelength when a spectrometer whose resolution is 0.
The orbital radius is proportional to n 2 See Equation 4. A beam of electrons enters a uniform 1. Find the possible angles between the z axis and the direction of the spin angular-momentum vector S. The nuclei of ordinary helium atoms, , contain two protons and two neutrons each; the nuclei of another type of helium atom, , contain two protons and one neutron each.
The properties of liquid and liquid are different because one type of helium atom obeys the exclusion principle but the other does not. Which is which, and why? Such atoms do not obey the exclusion principle. In what way does the electron structure of an alkali metal atom differ from that of a halogen atom? From that of an inert gas atom? A halogen atom lacks one electron of having a closed outer shell: An inert gas atom has a closed outer shell.
How many electrons can occupy an f subshell? Each state can have two electrons of opposite spins, for a total of 14 electrons. Repeated use of Equation 7. All are in group 1 of the periodic table. Account for the decrease in ionization energy with increasing atomic number. The outermost electron in each of these atoms is further from the nucleus for higher atomic number, and hence has a successively lower binding energy.
Would you think that such an electron is relatively easy or relatively hard to detach from the atom?
This outer electron is then relatively hard to detach. Why are Cl atoms more chemically active than Cl - ions? In each of the following pairs of atoms, which would you expect to be larger in size?
If the total number of electrons were odd, the net spin would be nonzero, and the anomalous Zeeman effect would be observable. Why is the normal Zeeman effect observed only in atoms with an even number of electrons? Use these wavelengths to calculate the effective magnetic field experienced by the outer electron in the sodium atom as a result of its orbital motion.
If , what values of l are possible? What must be true of the subshells of an atom which has a 1 S 0 ground state? There axe no other allowed states. This state has the lowest possible values of L and J , and is the only possible ground state. The lithium atom has one 2s electron outside a filled inner shell. The aluminum atom has two 3s electrons and one 3p electron outside filled inner shells.
Find the term symbol of its ground state. Answer the questions of Exercise 34 for an f electron in an atom whose total angular momentum is provided by this electron. How many substates are there for a given value of J?
What is the energy difference between different substates? Explain why the x-ray spectra of elements of nearby atomic numbers are qualitatively very similar, although the optical spectra of these elements may differ considerably. 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. If one of the characteristic wavelengths of the light the galaxy emits is nm.
For this problem. A galaxy in the constellation Ursa Major is receding from the earth at The classical and relativistic frequencies.
For the classical effect. 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. Inha University Department of Physics. The denominator will be indistinguishable from 1 at low speed. 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.
For an approaching source. For a receding source. 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. The distance 5 is the product vt. A burst of electromagnetic radiation of energy Eo is emitted by one end of the box.