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Fundamentals of Physics 10th Extended edition Jearl Walker, Halliday Resnick - Solutions

A laser emits at 424 nm in a single pulse that lasts 0.500 μs. The power of the pulse is 2.80 MW. If we assume that the atoms contributing to the pulse underwent stimulated emission only once during the 0.500 μs, how many atoms contributed?
A helium-neon laser emits laser light at a wavelength of 632.8 nm and a power of 2.3 mW. At what rate are photons emitted by this device?
A certain gas laser can emit light at wavelength 550 nm, which involves population inversion between ground state and an excited state. At room temperature, how many moles of neon are needed to put 10 atoms in that excited state by thermal agitation?
A pulsed laser emits light at a wavelength of 694.4 nm. The pulse duration is 12 ps, and the energy per pulse is 0.150 J. (a) What is the length of the pulse? (b) How many photons are emitted in each pulse?
A population inversion for two energy levels is often described by assigning a negative Kelvin temperature to the system. What negative temperature would describe a system in which the population of the upper energy level exceeds that of the lower level by 10% and the energy difference between the
A hypothetical atom has two energy levels, with a transition wavelength between them of 580 nm. In a particular sample at 300 K, 4.0 x 1020 such atoms are in the state of lower energy. (a) How many atoms are in the upper state, assuming conditions of thermal equilibrium? (b) Suppose, instead,
The mirrors in the laser of Fig. 40-20, which are separated by 8.0 cm, form an optical cavity in which standing waves of laser light can be set up. Each standing wave has an integral number n of half wavelengths in the 8.0 cm length, where n is large and the waves differ slightly in wavelength.
Figure 40-24 shows the energy levels of two types of atoms. Atoms A are in one tube, and atoms B are in another tube. The energies (relative to ground-state energy of zero) are indicated; the average lifetime of atoms in each level is also indicated. All the atoms are initially pumped to levels
How many electron states are in these sub-shells: (a) n = 4, l = 3 (b) n = 3, l = 1 (c) n = 4, l = 1 (d) n = 2, l = 0?
The beam from an argon laser (of wavelength 515 nm) has a diameter d of 3.00 mm and a continuous energy output rate of 5.00W. The beam is focused onto a diffuse surface by a lens whose focal length f is 3.50 cm. A diffraction pattern such as that of Fig. 36-10 is formed, the radius of the central
The active medium in a particular laser that generates laser light at a wavelength of 694 nm is 6.00 cm long and 1.00 cm in diameter. (a) Treat the medium as an optical resonance cavity analogous to a closed organ pipe. How many standing-wave nodes are there along the laser axis? (b) By what amount
Ruby lases at a wavelength of 694 nm. A certain ruby crystal has 4.00 x 1019 Cr ions (which are the atoms that lase).The lasing transition is between the first excited state and the ground state, and the output is a light pulse lasting 2.00 μs. As the pulse begins, 60.0% of the Cr ions are in the
Figure 40-25 is an energy-level diagram for a fictitious three-dimensional infinite potential well that contains one electron. The number of degenerate states of the levels is indicated: "non" means non-degenerate (which includes the ground state) and "triple" means 3 states. If we put a total of
Where sunlight shines on the atmosphere of Mars, carbon dioxide molecules at an altitude of about 75 km undergo natural laser action. The energy levels involved in the action are shown in Fig. 40-26; population inversion occurs between energy levels E2 and E1.(a) What wavelength of sunlight excites
Excited sodium atoms emit two closely spaced spectrum lines called the sodium doublet (Fig. 40-27) with wavelengths 588.995 nm and 589.592 nm.(a) What is the difference in energy between the two upper energy levels (n = 3, l = 1)?(b) This energy difference occurs because the electron's spin
When a comet approaches the Sun, the increased warmth evaporates water from the ice on the surface of the comet nucleus, producing a thin atmosphere of water vapor around the nucleus. Sunlight can then dissociate H2O molecules in the vapor to H atoms and OH molecules. The sunlight can also excite
By measuring the go-and-return time for a laser pulse to travel from an Earth-bound observatory to a reflector on the Moon, it is possible to measure the separation between these bodies. (a) What is the predicted value of this time? (b) The separation can be measured to a precision of about 15
Can an incoming intercontinental ballistic missile be destroyed by an intense laser beam? A beam of intensity 108 W/m2 would probably burn into and destroy a non-spinning missile in 1 s. (a) If the laser had 5.0 MW power, 3.0 mm wavelength, and a 4.0 m beam diameter (a very powerful laser indeed),
A molybdenum (Z = 42) target is bombarded with 35.0 keV electrons and the x-ray spectrum of Fig. 40-13 results. The KÎ² and Ka wavelengths are 63.0 and 71.0 pm, respectively. What photon energy corresponds to the(a) KÎ²(b) Ka radiation? The two radiations are to be filtered
An electron in a multi-electron atom is known to have the quantum number l = 3. What are its possible n, ml, and ms quantum numbers?
Show that if the 63 electrons in an atom of europium were assigned to shells according to the "logical" sequence of quantum numbers, this element would be chemically similar to sodium.
Lasers can be used to generate pulses of light whose durations are as short as 10 fs.(a) How many wavelengths of light (Î» = 500 nm) are contained in such a pulse?(b) InWhat is the missing quantity X (in years)?
Show that h = 1.06 x 10-34 J ∙ s = 6.59 x 10-16 eV ∙ s
Suppose that the electron had no spin and that the Pauli Exclusion Principle still held. Which, if any, of the present noble gases would remain in that category?
(A correspondence principle problem) Estimate (a) The quantum number for the orbital motion of Earth around the Sun (b) The number of allowed orientations of the plane of Earth's orbit. (c) Find θmin, the half-angle of the smallest cone that can be swept out by a perpendicular to Earth's orbit
In 1911, Ernest Rutherford modeled an atom as being a point of positive charge Ze surrounded by a negative charge -Ze uniformly distributed in a sphere of radius R centered at the point. At distance r within the sphere, the electric potential is(a) From this formula, determine the magnitude of
In the sub-shell l = 3, (a) What is the greatest (most positive) ml value? (b) How many states are available with the greatest ml value? (c) What is the total number of states available in the sub-shell?
An electron is in a state with l = 3.(c) What is the largest possible value of ml, (d) What multiple of h gives the corresponding value of Lz,(e) What multiple of Î¼B gives the corresponding value of Î¼othz? (g) The second largest possible value of ml (h) The smallest (that is, most negative)
What is the probability that, at a temperature of T = 300 K, an electron will jump across the energy gap Eg (= 5.5 eV) in a diamond that has a mass equal to the mass of Earth? Use the molar mass of carbon in Appendix F; assume that in diamond there is one valence electron per carbon atom.
In a simplified model of un doped semiconductor, the actual distribution of energy states may be replaced by one in which there are Nv states in the valence band, all these states having the same energy Ev, and Nc states in the conduction band, all these states having the same energy Ec. The number
What is the probability that a state 0.0620 eV above the Fermi energy will be occupied at (a) T = 0 K (b) T = 320 K?
An Î± particle (4He nucleus) is to be taken apart in the following steps. Give the energy (work) required for each step:(a) Remove a proton,(b) Remove a neutron,(c) Separate the remaining proton and neutron. For a particle, what are(d) The total binding energy and(e) The binding energy
A 10.2 MeV Li nucleus is shot directly at the center of a Ds nucleus. At what center-to-center distance does the Li momentarily stop, assuming the Ds does not move?
In a Rutherford scattering experiment, assume that an incident alpha particle (radius 1.80 fm) is headed directly toward a target gold nucleus (radius 6.23 fm).What energy must the alpha particle have to just barely "touch" the gold nucleus?
Large radio-nuclides emit an alpha particle rather than other combinations of nucleons because the alpha particle has such a stable, tightly bound structure. To confirm this statement, calculate the disintegration energies for these hypothetical decay processes and discuss the meaning of your
The radionuclide 11C decays according to 11C → 11B + e+ + v, T1/2 = 20.3 min. The maximum energy of the emitted positrons is 0.960 MeV. (a) Show that the disintegration energy Q for this process is given by Q = (mC - mB - 2me) c2, where mC and mB are the atomic masses of 11C and 11B,
The isotope 238U decays to 206Pb with a half-life of 4.47 x 109 y. Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead. That is, 238U → 206Pb + various decay products A rock is
A measurement of the energy E of an intermediate nucleus must be made within the mean lifetime Δt of the nucleus and necessarily carries an uncertainty ΔE according to the uncertainty principle ΔE ∙ Δt = h (a) What is the uncertainty E in the energy for an intermediate nucleus if the nucleus
Make a nuclidic chart similar to Fig. 42-6 for the 25 nuclides 118-122Te, 117-121Sb, 116-120Sn, 115-119In, and 114-118Cd. Draw in and label (a) All isobaric (constant A) lines (b) All lines of constant neutron excess, defined as N - Z.
The isotope 235U decays by alpha emission with a half-life of 7.0 ( 108 y. It also decays (rarely) by spontaneous fission, and if the alpha decay did not occur, its half-life due to spontaneous fission alone would be 3.0 ( 1017 y. (a) At what rate do spontaneous fission decays occur in 1.0 g of
Calculate the energy released in the fission reaction235U + n ( 141Cs + 93Rb + 2n.Here are some atomic and particle masses.
Calculate the disintegration energy for the fission of 52Cr into two equal fragments. The masses you will need are
Consider the fission of 238U by fast neutrons. In one fission event, no neutrons are emitted and the final stable end products, after the beta decay of the primary fission fragments, are 140Ce and 99Ru.(a) What is the total of the beta-decay events in the two beta-decay chains?
Assume that immediately after the fission of 236U according to Eq. 43-1, the resulting 140Xe and 94Sr nuclei are just touching at their surfaces. (a) Assuming the nuclei to be spherical, calculate the electric potential energy associated with the repulsion between the two fragments. (Use Eq. 42-3
A 236U nucleus undergoes fission and breaks into two middle- mass fragments, 140Xe and 96Sr.(a) By what percentage does the surface area of the fission products differ from that of the original 236U nucleus?(b) By what percentage does the volume change?
A 66 kiloton atomic bomb is fueled with pure 235U (Fig. 43-14), 4.0% of which actually undergoes fission.(a) What is the mass of the uranium in the bomb? (It is not 66 kilotons-that is the amount of released energy specified in terms of the mass of TNT required to produce the same amount of
In an atomic bomb, energy release is due to the uncontrolled fission of plutonium 239Pu (or 235U). The bomb's rating is the magnitude of the released energy, specified in terms of the mass of TNT required to produce the same energy release. One megaton of TNT releases 2.6 ( 1028 MeV of energy. (a)
In a particular fission event in which 235U is fissioned by slow neutrons, no neutron is emitted and one of the primary fission fragments is 83Ge. (a) What is the other fragment? The disintegration energy is = 170 MeV. How much of this energy goes to (b) the 83Ge fragment and (c) the other
A 200 MW fission reactor consumes half its fuel in 3.00 y. How much 235U did it contain initially? Assume that all the energy generated arises from the fission of 235U and that this nuclide is consumed only by the fission process.
The neutron generation time tgen in a reactor is the average time needed for a fast neutron emitted in one fission event to be slowed to thermal energies by the moderator and then initiate another fission event. Suppose the power output of a reactor at time t = 0 is P0. Show that the power output a
The thermal energy generated when radiation from radionuclides is absorbed in matter can serve as the basis for a small power source for use in satellites, remote weather stations, and other isolated locations. Such radionuclides are manufactured in abundance in nuclear reactors and may be
The neutron generation time tgen (see Problem 19) in a particular reactor is 1.0 ms. If the reactor is operating at a power level of 500 MW, about how many free neutrons are present in the reactor at any moment?
The neutron generation time (see Problem 19) of a particular reactor is 1.3 ms. The reactor is generating energy at the rate of 1200.0 MW. To perform certain maintenance checks, the power level must temporarily be reduced to 350.00 MW. It is desired that the transition to the reduced power level
Among the many fission products that may be extracted chemically from the spent fuel of a nuclear reactor is 90Sr (T1/2 = 29 y).This isotope is produced in typical large reactors at the rate of about 18 kg/y. By its radioactivity, the isotope generates thermal energy at the rate of 0.93 W/g.
(a) A neutron of mass mn and kinetic energy K makes a head-on elastic collision with a stationary atom of mass m. Show that the fractional kinetic energy loss of the neutron is given byFind (K/K for each of the following acting as the stationary atom:(b) Hydrogen,(c) Deuterium,(d) Carbon, and(e)
How long ago was the ratio 235U/238U in natural uranium deposits equal to 0.15?
The natural fission reactor discussed in Module 43-3 is estimated to have generated 15 gigawatt-years of energy during its lifetime. (a) If the reactor lasted for 200 000 y, at what average power level did it operate? (b) How many kilograms of 235U did it consume during its lifetime?
Some uranium samples from the natural reactor site described in Module 43-3 were found to be slightly enriched in 235U, rather than depleted. Account for this in terms of neutron absorption by the abundant isotope 238U and the subsequent beta and alpha decay of its products.
The uranium ore mined today contains only 0.72% of fissionable 235U, too little to make reactor fuel for thermal-neutron fission. For this reason, the mined ore must be enriched with 235U. Both 235U (T1/2 = 7.0 ( 108 y) and 238U (T1/2 = 4.5 ( 109 y) are radioactive. How far back in time would
A thermal neutron (with approximately zero kinetic energy) is absorbed by a 238U nucleus. How much energy is transferred from mass energy to the resulting oscillation of the nucleus? Here are some atomic masses and the neutron mass.
Verify that the fusion of 1.0 kg of deuterium by the reactionCould keep a 100 W lamp burning for 2.5 ( 104 y.
Calculate the height of the Coulomb barrier for the head-on collision of two deuterons, with effective radius 2.1 fm.
For overcoming the Coulomb barrier for fusion, methods other than heating the fusible material have been suggested. For example, if you were to use two particle accelerators to accelerate two beams of deuterons directly toward each other so as to collide head-on, (a) What voltage would each
Calculate the Coulomb barrier height for two 7Li nuclei that are fired at each other with the same initial kinetic energy K. (Use Eq. 42-3 to calculate the radii of the nuclei.)
In Fig. 43-10, the equation for n(K), the number density per unit energy for particles, isWhere n is the total particle number density. At the center of the Sun, the temperature is 1.50 ( 107 K and the average proton energy Kavg is 1.94 keV. Find the ratio of the proton number density at 5.00 keV
Assume that the protons in a hot ball of protons each have a kinetic energy equal to kT, where k is the Boltzmann constant and T is the absolute temperature. If T = 1 ( 107 K, what (approximately) is the least separation any two protons can have?
2H1 + 1H1 ( 3He2 + photonHere are some atomic masses.
The Sun has mass 2.0 ( 1030 kg and radiates energy at the rate 3.9 ( 1026 W. (a) At what rate is its mass changing? (b) What fraction of its original mass has it lost in this way since it began to burn hydrogen, about 4.5 ( 109 y ago?
We have seen that for the overall proton-proton fusion cycle is 26.7 MeV. How can you relate this number to the values for the reactions that make up this cycle, as displayed in Fig. 43-11?
Show that the energy released when three alpha particles fuse to form 12C is 7.27 MeV. The atomic mass of 4He is 4.0026 u, and that of 12C is 12.0000 u.
The fission properties of the plutonium isotope 239Pu are very similar to those of 235U. The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1.00 kg of pure 239Pu undergo fission?
Calculate and compare the energy released by (a) the fusion of 1.0 kg of hydrogen deep within the Sun and (b) the fission of 1.0 kg of 235U in a fission reactor.
A star converts all its hydrogen to helium, achieving a 100% helium composition. Next it converts the helium to carbon via the triple-alpha process,4He + 4He + 4He ( 12C + 7.27 MeV.The mass of the star is 4.6 ( 1032 kg, and it generates energy at the rate of 5.3 ( 1030 W. How long will it take to
(Distinguish carefully between atomic and nuclear masses, and take the positrons properly into account.)
Figure 43-15 shows an early proposal for a hydrogen bomb. The fusion fuel is deuterium, 2H.The high temperature and particle density needed for fusion are provided by an atomic bomb "trig-ger" that involves a 235U or 239Pu fission fuel arranged to impress an imploding, compressive shock wave on the
Assume that the core of the Sun has one-eighth of the Sun's mass and is compressed within a sphere whose radius is one-fourth of the solar radius.Assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun's energy is generated there. If the Sun
(a) Calculate the rate at which the Sun generates neutrinos. Assume that energy production is entirely by the proton-proton fusion cycle. (b) At what rate do solar neutrinos reach Earth?
In certain stars the carbon cycle is more effective than the proton-proton cycle in generating energy. This carbon cycle is(a) Show that this cycle is exactly equivalent in its overall effects to the proton-proton cycle of Fig. 43-11.
Coal burns according to the reaction C + O2 ( CO2. The heat of combustion is 3.3 ( 107 J/kg of atomic carbon consumed. (a) Express this in terms of energy per carbon atom. (b) Express it in terms of energy per kilogram of the initial reactants, carbon and oxygen. (c) Suppose that the Sun (mass =
Verify the values reported in Eqs. 43-13, 43-14, and 43-15. The needed masses are
Roughly 0.0150% of the mass of ordinary water is due to "heavy water," in which one of the two hydrogens in an H2O molecule is replaced with deuterium, 2H. How much average fusion power could be obtained if we "burned" all the 2H in 1.00 liter of water in 1.00 day by somehow causing the deuterium
During the Cold War, the Premier of the Soviet Union threatened the United States with 2.0 megaton 239Pu warheads. (Each would have yielded the equivalent of an explosion of 2.0 megatons of TNT, where 1 megaton of TNT releases 2.6 ( 1028 MeV of energy.) If the plutonium that actually fissioned had
(a) Express this as energy per kilogram of hydrogen consumed.(b) The power of the Sun is 3.9 ( 1026 W. If its energy derives from the proton-proton cycle, at what rate is it losing hydrogen?(c) At what rate is it losing mass?(d) Account for the difference in the results for (b) and (c).(e) The mass
Many fear that nuclear power reactor technology will increase the likelihood of nuclear war because reactors can be used not only to produce electrical energy but also, as a by-product through neutron capture with inexpensive 238U, to make 239Pu, which is a "fuel" for nuclear bombs. What simple
In the deuteron-triton fusion reaction of Eq. 43-15, what is the kinetic energy of (a) the alpha particle and (b) the neutron? Neglect the relatively small kinetic energies of the two combining particles.
Verify that, as reported in Table 43-1, fissioning of the 235U in 1.0 kg of UO2 (enriched so that 235U is 3.0% of the total uranium) could keep a 100 W lamp burning for 690 y.
At the center of the Sun, the density of the gas is 1.5 ( 105 kg/m3 and the composition is essentially 35% hydrogen by mass and 65% helium by mass. (a) What is the number density of protons there? (b) What is the ratio of that proton density to the density of particles in an ideal gas at standard
Expressions for the Maxwell speed distribution for molecules in a gas are given in Chapter 19.(a) Show that the most probable energy is given byVerify this result with the energy distribution curve of Fig. 43-10, for which T = 1.5 ( 107 K. (b) Show that the most probable speed is given by Find its
The uncompressed radius of the fuel pellet of Sample Problem 43.05 is 20 (m. Suppose that the compressed fuel pellet "burns" with an efficiency of 10%-that is, only 10% of the deuterons and 10% of the tritons participate in the fusion reaction of Eq. 43-15. (a) How much energy is released in each
Assume that a plasma temperature of 1 ( 108 K is reached in a laser-fusion device. (a) What is the most probable speed of a deuteron at that temperature? (b) How far would such a deuteron move in a confinement time of 1 ( 10-12 s?
(a) - (d) Complete the following table, which refers to the generalized fission reaction 235U + n ( X + Y + bn.
At what rate must 235U nuclei undergo fission by neutron bombardment to generate energy at the rate of 1.0 W? Assume that = 200 MeV.
(a) Calculate the disintegration energy for the fission of the molybdenum isotope 98Mo into two equal parts. The masses you will need are 97.905 41 u for 98Mo and 48.950 02 u for 49Sc.(b) If turns out to be positive, discuss why this process does not occur spontaneously.
(a) How many atoms are contained in 1.0 kg of pure 235U?(c) For how long would this energy light a 100 W lamp?
A positively charged pion decays by Eq. 44-7: (+ ( (+ + v. What must be the decay scheme of the negatively charged pion? (The (- is the antiparticle of the (+.)
A neutral pion has a rest energy of 135 MeV and a mean life of 8.3 ( 10-17 s. If it is produced with an initial kinetic energy of 80 MeV and decays after one mean lifetime, what is the longest possible track this particle could leave in a bubble chamber? Use relativistic time dilation.
Which conservation law is violated in each of these proposed decays? Assume that the initial particle is stationary and the decay products have zero orbital angular momentum.(a) (¯ ( e¯ + v(;(b) (¯ ( e+ + ve + v̅(;(c) ( + ( (+ + v(.
The A2+ particle and its products decay according to the scheme(a) What are the final stable decay products? From the evidence,(b) Is the A2+ particle a fermion or a boson and(c) Is it a meson or a baryon?(d) What is its baryon number?
Show that if, instead of plotting strangeness S versus charge q for the spin - 1/2 baryons in Fig. 44-3a and for the spin-zero mesons in Fig. 44-3b, we plot the quantity Y = B + S versus the quantity Tz = q - 1/2(B + S), we get the hexagonal patterns without using sloping axes. (The quantity Y is
Calculate the disintegration energy of the reactions (a) (+ + p ( (+ + K+ and (b) K- + p ( (0 + (0.

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