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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

(a) The planet Pluto and its Moon Charon are separated by 19,600 km. Neglecting atmospheric effects, should the 5.08-m-diameter Mount Palomar telescope be able to resolve these bodies when they are 4.50 x 109 km from Earth? Assume an average wavelength of 550 nm. (b) In actuality, it is just
The headlights of a car are 1.3 m apart. What is the maximum distance at which the eye can resolve these two headlights? Take the pupil diameter to be 0.40 cm.
When dots are placed on a page from a laser printer, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh’s criterion. Take the pupil of the eye to be 3.0 mm and the distance from the paper to the eye of 35
Consider diffraction limits for an electromagnetic wave interacting with a circular object. Construct a problem in which you calculate the limit of angular resolution with a device, using this circular object (such as a lens, mirror, or antenna) to make observations. Also calculate the limit to
A soap bubble is 100 nm thick and illuminated by white light incident perpendicular to its surface. What wavelength and color of visible light is most constructively reflected, assuming the same index of refraction as water?
An oil slick on water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?
Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Take the blue wavelength to be 470 nm and the index of refraction of oil to be 1.40.
A film of soapy water (n = 1.33) on top of a plastic cutting board has a thickness of 233 nm. What color is most strongly reflected if it is illuminated perpendicular to its surface?
What are the three smallest non-zero thicknesses of soapy water (n = 1.33) on Plexiglas if it appears green (constructively reflecting 520-nm light) when illuminated perpendicularly by white light? Explicitly show how you follow the steps in Problem Solving Strategies for Wave Optics.
Suppose you have a lens system that is to be used primarily for 700-nm red light. What is the second thinnest coating of fluorite (magnesium fluoride) that would be non-reflective for this wavelength?
(a) Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of light were only 45.0 m/s. (b) Find the ratio of the relativistic kinetic energy to classical.
(a) What is the energy in joules and electron volts of a photon of 420-nm violet light?(b) What is the maximum kinetic energy of electrons ejected from calcium by 420-nm violet light, given that the binding energy (or work function) of electrons for calcium metal is 2.71 eV?StrategyTo solve part
(a) Calculate the momentum of a visible photon that has a wavelength of 500 nm.(b) Find the velocity of an electron having the same momentum. (c) What is the energy of the electron, and how does it compare with the energy of the photon?StrategyFinding the photon momentum is a straightforward
Show that p = E/c for the photon considered in the Example 29.5.StrategyWe will take the energy found in Example 29.5, divide it by the speed of light, and see if the same momentum is obtained as before.Data from Example 29.5Calculate the momentum of a visible photon that has a wavelength of 500
Calculate the approximate energy of a Kα x ray from a tungsten anode in an x-ray tube.StrategyHow do we calculate energies in a multiple-electron atom? In the case of characteristic x rays, the following approximate calculation is reasonable. Characteristic x rays are produced when an inner-shell
Show that (13.6 eV)/hc = 1.097 x 107 m = R (Rydberg's constant), as discussed in the text.
Some of the most powerful lasers are based on the energy levels of neodymium in solids, such as glass, as shown in Figure 30.60.(a) What average wavelength light can pump the neodymium into the levels above its metastable state? (b) Verify that the 1.17 eV transition produces 1.06μm
Repeat the previous exercise for l = 3.Data from previous Question(a) What is the magnitude of the angular momentum for an l = 1 electron?(b) Calculate the magnitude of the electron's spin angular momentum. (c) What is the ratio of these angular momenta?
Which of the following spectroscopic notations are not allowed?(a) 5s1(b) 1d1(c) 4s3(d) 3p7(e) 5g15State which rule is violated for each that is not allowed.
Consider the Doppler-shifted hydrogen spectrum received from a rapidly receding galaxy. Construct a problem in which you calculate the energies of selected spectral lines in the Balmer series and examine whether they can be described with a formula like that in the equation , but with a different
Verify that a 2.3 x 1017 kg mass of water at normal density would make a cube 60 km on a side, as claimed in Example 31.1. (This mass at nuclear density would make a cube 1.0 m on a side.)Data from Example 31.1Find the radius of an iron-56 nucleus.Find its approximate density in kg/m3,
When a nucleus α decays, does the α particle move continuously from inside the nucleus to outside? That is, does it travel each point along an imaginary line from inside to out? Explain.
Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for β- decay given in the equation To do this, identify the values of each before and after the decay. A 2XN2+1 YN-1 +B³²¯ + V₂. ve.
When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum.(a) Confirm that the annihilation equation e+ + e- → γ + γ conserves charge, electron family number, and total number of nucleons. To do this, identify the values of
Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for β- decay given in the equation To do this, identify the values of each before and after the decay. A 2XN2-1YN-1 +B³²¯¯ +ve.
Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equationTo do this, identify the values of each before and after the capture. Z A XN+eYN+1 +ve.
Neutrons from a source (perhaps the one discussed in the preceding problem) bombard natural molybdenum, which is 24 percent 98Mo. What is the energy output of the reaction ? The mass of 98Mo is given in Appendix A: Atomic Masses, and that of 99Mo is 98.907711 u.Data from Appendix A 98 Mo + n 99 Mo
A neutron generator uses an α source, such as radium, to bombard beryllium, inducing the reaction Such neutron sources are called RaBe sources, or PuBe sources if they use plutonium to get the α s. Calculate the energy output of the reaction in MeV. 4He + Be ¹2C + n.
(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture.(b) If this takes place continuously over a period of a year, what is the average power
Calculate the dose in rem/y for the lungs of a weapons plant employee who inhales and retains an activity of 1.00 μCi of 239Pu in an accident. The mass of affected lung tissue is 2.00 kg, the plutonium decays by emission of a 5.23-MeV α particle, and you may assume the higher value of the RBE for
In terms of radiation dose, what is the major difference between medical diagnostic uses of radiation and medical therapeutic uses?
Calculate the energy released in the following spontaneous fission reaction:StrategyAs always, the energy released is equal to the mass destroyed times c2, so we must find the difference in mass between the parent 238U and the fission products. 238 SU 95 Sr+ 140 Xe + 3n 32.26
One of the methods used to limit radiation dose to the patient in medical imaging is to employ isotopes with short half-lives. How would this limit the dose?
The purpose of producing 99Mo (usually by neutron activation of natural molybdenum, as in the preceding problem) is to produce 99mTc. Using the rules, verify that the β- decay of 99Mo produces 99mTc. (Most 99mTc nuclei produced in this decay are left in a metastable excited state denoted 99mTc.)
Isotopes that emit radiation are relatively safe outside the body and exceptionally hazardous inside. Yet those that emit γ radiation are hazardous outside and inside. Explain why.
Table 32.1 indicates that 7.50 mCi of 99mTc is used in a brain scan. What is the mass of technetium?Data from Table 32.1 Procedure, isotope Brain scan 99m nTe 113m In 11C (PET) 13N (PET) 150 (PET) 18 F (PET) Lung scan 99m Tc 133 Xe 1311 99m Typical activity (mCi), where 1 mCi = 3.7 x 107
(a) Two annihilation rays in a PET scan originate at the same point and travel to detectors on either side of the patient. If the point of origin is 9.00 cm closer to one of the detectors, what is the difference in arrival times of the photons? (This could be used to give position information, but
Why is radon more closely associated with inducing lung cancer than other types of cancer?
(a) Neutron activation of sodium, which is 100% 23Na, produces 24Na, which is used in some heart scans, as seen in Table 32.1. The equation for the reaction is Find its energy output, given the mass of 24Na is 23.990962 u.(b) What mass of 24Na produces the needed 5.0-mCi activity, given its
Which methods of radiation protection were used in the device shown in the first photo in Figure 32.30? Which were used in the situation shown in the second photo? (a) (b)
The RBE for low-energy βs is 1.7, whereas that for higher-energy βs is only 1. Explain why, considering how the range of radiation depends on its energy.
What radioisotope could be a problem in homes built of cinder blocks made from uranium mine tailings? (This is true of homes and schools in certain regions near uranium mines.)
What is the dose in mSv for:(a) A 0.1 Gy x-ray?(b) 2.5 mGy of neutron exposure to the eye?(c) 1.5 mGy of exposure?
Are some types of cancer more sensitive to radiation than others? If so, what makes them more sensitive?
Find the radiation dose in Gy for:(a) A 10-mSv fluoroscopic x-ray series.(b) 50 mSv of skin exposure by an a emitter.(c) 160 mSv of β- and γ rays from the 40K in your body.
Suppose a person swallows some radioactive material by accident. What information is needed to be able to assess possible damage?
How many Gy of exposure is needed to give a cancerous tumor a dose of 40 Sv if it is exposed to α activity?
Radiotherapy is more likely to be used to treat cancer in elderly patients than in young ones. Explain why. Why is radiotherapy used to treat young people at all?
What is the dose in Sv in a cancer treatment that exposes the patient to 200 Gy of rays?
Does food irradiation leave the food radioactive? To what extent is the food altered chemically for low and high doses in food irradiation?
One half the γ rays from 99mTc are absorbed by a 0.170-mm-thick lead shielding. Half of the γ rays that pass through the first layer of lead are absorbed in a second layer of equal thickness. What thickness of lead will absorb all but one in 1000 of these γ rays?
Compare a low dose of radiation to a human with a low dose of radiation used in food treatment.
A plumber at a nuclear power plant receives a whole-body dose of 30 mSv in 15 minutes while repairing a crucial valve. Find the radiationinduced yearly risk of death from cancer and the chance of genetic defect from this maximum allowable exposure.
137Cs Suppose one food irradiation plant uses a source while another uses an equal activity of 60Co. Assuming equal fractions of the γ rays from the sources are absorbed, why is more time needed to get the same dose using the 137Cs source?
In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well-known safety of microwave radiation. Find the energy in MeV of a photon having a wavelength of a picometer.
Why does the fusion of light nuclei into heavier nuclei release energy?
Find the mass of 239Pu that has an activity of 1.00 μCi.
Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.
In considering potential fusion reactions, what is the advantage of the reaction 2H+ 3H-4He 2H+2H³He + n over the reaction + n?
A beam of 168-MeV nitrogen nuclei is used for cancer therapy. If this beam is directed onto a 0.200-kg tumor and gives it a 2.00-Sv dose, how many nitrogen nuclei were stopped?
Give reasons justifying the contention made in the text that energy from the fusion reaction 2H+ 2H → He + y is relatively difficult to capture and utilize.
(a) If the average molecular mass of compounds in food is 50.0 g, how many molecules are there in 1.00 kg of food? (b) How many ion pairs are created in 1.00 kg of food, if it is exposed to 1000 Sv and it takes 32.0 eV to create an ion pair? (c) Find the ratio of ion pairs to molecules. (d) If
Calculate the dose in Sv to the chest of a patient given an x-ray under the following conditions. The x-ray beam intensity is 1.50 W/m2, the area of the chest exposed is 0.0750 m2, 35.0% of the x-rays are absorbed in 20.0 kg of tissue, and the exposure time is 0.250 s.
Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?
(a) A cancer patient is exposed to γ rays from a 5000-Ci 60Co transillumination unit for 32.0 s. The γ rays are collimated in such a manner that only 1.00% of them strike the patient. Of those, 20.0% are absorbed in a tumor having a mass of 1.50 kg. What is the dose in rem to the tumor, if the
Explain, in terms of conservation of momentum and energy, why collisions of neutrons with protons will thermalize neutrons better than collisions with oxygen.
What is the mass of 60Co in a cancer therapy transillumination unit containing 5.00 kCi of 60Co?
The ruins of the Chernobyl reactor are enclosed in a huge concrete structure built around it after the accident. Some rain penetrates the building in winter, and radioactivity from the building increases. What does this imply is happening inside?
Since the uranium or plutonium nucleus fissions into several fission fragments whose mass distribution covers a wide range of pieces, would you expect more residual radioactivity from fission than fusion? Explain.
Naturally occurring 40K is listed as responsible for 16 mrem/y of background radiation. Calculate the mass of 40K that must be inside the 55-kg body of a woman to produce this dose. Each 40K decay emits a 1.32-MeV β, and 50% of the energy is absorbed inside the body.
The core of a nuclear reactor generates a large amount of thermal energy from the decay of fission products, even when the power-producing fission chain reaction is turned off. Would this residual heat be greatest after the reactor has run for a long time or short time? What if the reactor has been
(a) Background radiation due to 226Ra averages only 0.01 mSv/y, but it can range upward depending on where a person lives. Find the mass of 226Ra in the 80.0-kg body of a man who receives a dose of 2.50-mSv/y from it, noting that each 226Ra decay emits a 4.80-MeV a particle. You may neglect dose
How can a nuclear reactor contain many critical masses and not go supercritical? What methods are used to control the fission in the reactor?
The annual radiation dose from 14C in our bodies is 0.01 mSv/y. Each 14C decay emits a β- averaging 0.0750 MeV. Taking the fraction of 14C to be 1.3 x 10-12 N of normal 12C, and assuming the body is 13% carbon, estimate the fraction of the decay energy absorbed. (The rest escapes, exposing those
Why can heavy nuclei with odd numbers of neutrons be induced to fission with thermal neutrons, whereas those with even numbers of neutrons require more energy input to induce fission?
If everyone in Australia received an extra 0.05 mSv per year of radiation, what would be the increase in the number of cancer deaths per year? (Assume that time had elapsed for the effects to become apparent.) Assume that there are 200 x 10-4 deaths per Sv of radiation per year. What percent of the
Why is a conventional fission nuclear reactor not able to explode as a bomb?
What are some of the reasons that plutonium rather than uranium is used in all fission bombs and as the trigger in all fusion bombs?
Calculate the energy output in each of the fusion reactions in the proton-proton cycle, and verify the values given in the above summary.Summary:
Show that the total energy released in the proton-proton cycle is 26.7 MeV, considering the overall effect inand being certain to include the annihilation energy. ¹H+¹H2H+e+ + Uc ¹H+2H³He + y, and 3 He + ³ He → 4He + ¹H+ ¹H
Use the laws of conservation of momentum and energy to explain how a shape charge can direct most of the energy released in an explosion in a specific direction. (Note that this is similar to the situation in guns and cannons—most of the energy goes into the bullet.)
How does the lithium deuteride in the thermonuclear bomb shown in Figure 32.28 supply tritium (3H) as well as deuterium (2H)?Data from figure 32.28 238U 2:39 Pu Reflector and fission material (fast ns) Beryllium neutron reflector Shape charges Lithium deuteride 239 Pu and 235U Styrofoam with y
Verify by listing the number of nucleons, total charge, and electron family number before and after the cycle that these quantities are conserved in the overall proton-proton cycle in 2e +4¹ H He + 20e + 6y.
Tritium is naturally rare, but can be produced by the reaction How much energy in MeV is released in this neutron capture? n+²H → ³H+%.
Fallout from nuclear weapons tests in the atmosphere is mainly 90Sr and 137Cs, which have 28.6-and 32.2-y half-lives, respectively. Atmospheric tests were terminated in most countries in 1963, although China only did so in 1980. It has been found that environmental activities of these two isotopes
Two fusion reactions mentioned in the text areBoth reactions release energy, but the second also creates more fuel. Confirm that the energies produced in the reactions are 20.58 and 2.22 MeV, respectively. Comment on which product nuclide is most tightly bound, 4He or 2H. n+³ He → *He +
(a) Calculate the number of grams of deuterium in an 80,000-L swimming pool, given deuterium is 0.0150% of natural hydrogen.(b) Find the energy released in joules if this deuterium is fused via the reaction(c) Could the neutrons be used to create more energy?(d) Discuss the amount of this type of
How many kilograms of water are needed to obtain the 198.8 mol of deuterium, assuming that deuterium is 0.01500% (by number) of natural hydrogen?
Another set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It isWrite down the overall effect of the carbon cycle (as was done for the proton-proton cycle inNote the number of protons (1H) required and assume that
The power output of the Sun is 4 x 1026 W.(a) If 90% of this is supplied by the proton-proton cycle, how many protons are consumed per second?(b) How many neutrinos per second should there be per square meter at the Earth from this process? This huge number is indicative of how rarely a neutrino
(a) Find the total energy released in MeV in each carbon cycle (elaborated in the above problem) including the annihilation energy.(b) How does this compare with the proton-proton cycle output?Data from Problem 36Another set of reactions that result in the fusing of hydrogen into helium in the Sun
Find the amount of energy given to the 4He nucleus and to the γ ray in the reactionusing the conservation of momentum principle and taking the reactants to be initially at rest. This should confirm the contention that most of the energy goes to the γ ray. n+³ n+3 He4 He + %,
The laser system tested for inertial confinement can produce a 100-kJ pulse only 1.00 ns in duration. (a) What is the power output of the laser system during the brief pulse?(b) How many photons are in the pulse, given their wavelength is 1.06 μm? (c) What is the total momentum of all these
(a) What temperature gas would have atoms moving fast enough to bring two 3He nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another.(b) Does this
(a) Calculate the energy released in the neutron-induced fission (similar to the spontaneous fission in Example 32.3)(b) This result is about 6 MeV greater than the result for spontaneous fission. Why?(c) Confirm that the total number of nucleons and total charge are conserved in this reaction.Data
(a) Estimate the years that the deuterium fuel in the oceans could supply the energy needs of the world. Assume world energy consumption to be ten times that of the United States which is 8 x 1019 J/y and that the deuterium in the oceans could be converted to energy with an efficiency of 32%. You
Breeding plutonium produces energy even before any plutonium is fissioned. (The primary purpose of the four nuclear reactors at Chernobyl was breeding plutonium for weapons. Electrical power was a by-product used by the civilian population.) Calculate the energy produced in each of the reactions
The naturally occurring radioactive isotope 232Th does not make good fission fuel, because it has an even number of neutrons; however, it can be bred into a suitable fuel (much as 238U is bred into 239P).(a) What are Z and N for 232Th? (b) Write the reaction equation for neutron captured by 232Th
The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0% efficiency in converting nuclear power to electrical. (a) What is the thermal nuclear power output in megawatts?(b) How many 235U nuclei fission each second, assuming the average fission produces 200
A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity in curies?

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