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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

a. What are the x- and y-components of vectorshown in FIGURE EX3.3 in terms of the angle u and the magnitude E?b. For the same vector, what are the x- and y-components in terms of the angle f and the magnitude E?Figure Ex 3.3
Trace the vectors in Figure Ex 3.2 into your paper. Then find(a)and(b)Figure Ex 3.2
Trace the vectors in FIGURE EX3.1 onto your paper. Then find(a)and(b)Figure Ex 3.1
How would you define the zero vector
For each, show how or explain why not.IfCan C = 0? Can C
For each, show how or explain why not.If CanCan
The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver’s reaction time of 0.50 s. What is the minimum stopping distance for the same car traveling at a speed of 40 m/s?
Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall.a. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?b. What is the bearing’s impact velocity?
It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let’s analyze the decay of a free neutron that is at rest in the
All the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced into the gases from which the sun and the planets of our solar system were formed. Nuclear physics suggests that
The uranium isotope 238U is naturally present at low levels in many soils. One of the nuclei in the decay series of 238U is the radon isotope 222Rn, which decays by emitting a 5.50 MeV alpha particle with t1/2 = 3.82 days. Radon is a gas, and it tends to seep from soil into basements. The
The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40K has a 1.28 billion-year half-life and is naturally present at very low levels. 40K decays by two routes: 89% undergo beta-minus decay into 40Ca while 11% undergo electron capture to become 40Ar.
A chest x ray uses 10 keV photons with an RBE of 0.85. A 60 kg person receives a 0.30 mSv dose from one chest x ray that exposes 25% of the patient’s body. How many x ray photons are absorbed in the patient’s body?
Radioactive isotopes often occur together in mixtures. Suppose a 100 g sample contains 131Ba, with a half-life of 12 days, and 47Ca, with a half-life of 4.5 days. If there are initially twice as many calcium atoms as there are barium atoms, what will be the ratio of calcium atoms to barium atoms
The half-life of the uranium isotope 235U is 700 million years. The earth is approximately 4.5 billion years old. How much more 235U was there when the earth formed than there is today? Give your answer as the then-to-now ratio.
A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50 hour. What is the half-life of B?
How many half-lives must elapse until(a) 90%(b) 99% of a radioactive sample of atoms has decayed?
A 115 mCi radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital 16 hours later its activity is 95 mCi. The lowest usable level of activity is 10 mCi.a. What is the tracer’s half-life?b. For how long after delivery is the sample usable?
137Cs is a common product of nuclear fission. Suppose an accident spills 550 mCi of 137Cs in a lab room.a. What mass of 137Cs is spilled?b. If the spill is not cleaned up, how long will it take until the radiation level drops to an acceptable level, for a room this size, of 25 mCi?
A 1 Ci source of radiation is a significant source. 238U is an alpha emitter. What mass of 238U has an activity of 1 Ci?
What is the age in years of a bone in which the 14C/12C ratio is measured to be 1.65 × 10-13?
The activity of a sample of the cesium isotope 137Cs, with a half-life of 30 years, is 2.0 × 108 Bq. Many years later, after the sample has fully decayed, how many beta particles will have been emitted?
What energy (in MeV) alpha particle has a de Broglie wavelength equal to the diameter of a 238U nucleus?
Use the graph of binding energy to estimate the total energy released if a nucleus with mass number 240 fissions into two nuclei with mass number 120.
Could a 56Fe nucleus fission into two 28Al nuclei? Your answer, which should include some calculations, should be based on the curve of binding energy.
Use the graph of binding energy to estimate the total energy released if three 4He nuclei fuse together to form a 12C nucleus.
You learned in Chapter 41 that the binding energy of the electron in a hydrogen atom is 13.6 eV.a. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.b. By
The element gallium has two stable isotopes: 69Ga with an atomic mass of 68.92 u and 71Ga with an atomic mass of 70.92 u. A periodic table shows that the chemical atomic mass of gallium is 69.72 u. What is the percent abundance of 69Ga?
a. What initial speed must an alpha particle have to just touch the surface of a 197Au gold nucleus before being turned back? Assume the nucleus stays at rest.b. What is the initial energy (in MeV) of the alpha particle?
Particle accelerators fire protons at target nuclei so that investigators can study the nuclear reactions that occur. In one experiment, the proton needs to have 20 MeV of kinetic energy as it impacts a 207Pb nucleus. With what initial kinetic energy (in MeV) must the proton be fired toward the
A 50 kg laboratory worker is exposed to 20 mJ of beta radiation with RBE = 1.5. What is the dose equivalent in mrem?
1.5 Gy of gamma radiation are directed into a 150 g tumor during radiation therapy. How much energy does the tumor absorb?
What is the total energy (in MeV) released in the beta decay of a neutron?
What is the total energy (in MeV) released in the beta-minus decay of 3H?
What is the total energy (in MeV) released in the beta-minus decay of 24Na?
What is the energy (in MeV) released in the alpha decay of 239Pu?
An unstable nucleus undergoes alpha decay with the release of 5.52 MeV of energy. The combined mass of the parent and daughter nuclei is 452 u. What was the parent nucleus?
a. What are the isotopic symbols of all A = 19 isobars?b. Which of these are stable nuclei?c. For those that are not stable, identify both the decay mode and the daughter nucleus.
a. What are the isotopic symbols of all A = 17 isobars?b. Which of these are stable nuclei?c. For those that are not stable, identify both the decay mode and the daughter nucleus.
The half-life of 60Co is 5.27 years. The activity of a 60Co sample is 3.50 × 109 Bq. What is the mass of the sample?
What is the half-life in days of a radioactive sample with 5.0 × 1015 atoms and an activity of 5.0 × 108 Bq?
The radioactive hydrogen isotope 3H, called tritium, has a half-life of 12 years.a. What are the decay mode and the daughter nucleus of tritium?b. What are the lifetime and the decay rate of tritium?
A sample of 1.0 × 1010 atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?
The radium isotope 226Ra has a half-life of 1600 years. A sample begins with 1.00 × 1010 226Ra atoms. How many are left after(a) 200 years,(b) 2000 years,(c) 20,000 years?
Calculate the chemical atomic mass of silicon.
Calculate (in MeV) the binding energy per nucleon for 14O and 16O. Which is more tightly bound?
Calculate (in MeV) the binding energy per nucleon for 3He and 4He. Which is more tightly bound?
Calculate (in MeV) the total binding energy and the binding energy per nucleon for 129I and for 129Xe.
Calculate (in MeV) the total binding energy and the binding energy per nucleon for 3H and for 3He.
a. What is the smallest value of A for which there are two stable nuclei? What are they?b. For which values of A less than this are there no stable nuclei?
Calculate the mass, radius, and density of the nucleus of(a) 7Li(b) 207Pb.Give all answers in SI units.
Which stable nuclei have a diameter of 7.46 fm?
How many protons and how many neutrons are in(a) 3He,(b) 32P,(c) 32S,(d) 238U?
How many protons and how many neutrons are in(a) 6Li,(b) 54Cr,(c) 54Fe,(d) 220Rn?
The three isotopes 212Po, 137Cs, and 90Sr decay as 212Po → 208Pb + α, 137Cs → 137Ba + e- + γ, and 90Sr → 90Y + e-. Which of these isotopes would be most useful as a biological tracer? Why?
Nucleus A decays into nucleus B with a half-life of 10 s. At t = 0 s, there are 1000 A nuclei and no B nuclei. At what time will there be 750 B nuclei?
a. How do we know the strong force exists?b. How do we know the strong force is short range?
a. Is the binding energy of a nucleus with A = 200 more than, less than, or equal to the binding energy of a nucleus with A = 60? Explain.b. Is a nucleus with A = 200 more tightly bound, less tightly bound, or bound equally tightly as a nucleus with A = 60? Explain.
Consider the atoms 16O, 18O, 18F, 18Ne, and 20Ne. Some of the following questions may have more than one answer. Give all answers that apply.a. Which are isotopes?b. Which are isobars?c. Which have the same chemical properties?d. Which have the same number of neutrons?
An atom in an excited state has a 1.0% chance of emitting a photon in 0.20 ns. How long will it take for 25% of a sample of excited atoms to decay?
Find the distance, in terms of aB, between the two peaks in the radial probability density of the 2s state of hydrogen.
Prove that the most probable distance from the proton of an electron in the 2s state of hydrogen is 5.236aB.
What is the probability of finding a 1s hydrogen electron at distance r > aB from the proton?
The 1997 Nobel Prize in physics went to Steven Chu, Claude Cohen-Tannoudji, and William Phillips for their development of techniques to slow, stop, and “trap” atoms with laser light. To see how this works, consider a beam of rubidium atoms (mass 1.4 × 10-25 kg) traveling at 500 m/s after being
A ruby laser emits a 100 MW, 10-ns-long pulse of light with a wavelength of 690 nm. How many chromium atoms undergo stimulated emission to generate this pulse?
In fluorescence microscopy, an important tool in biology, a laser beam is absorbed by target molecules in a sample. These molecules are then imaged by a microscope as they emit longer-wavelength photons in quantum jumps back to lower energy levels, a process known as fluorescence. A variation on
a. Find an expression in terms of τ for the half-life t1/2 of a sample of excited atoms. The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon.b. What is the half-life of the 3p state of sodium?
a. What is the decay rate for the 2p state of hydrogen?b. During what interval of time will 10% of a sample of 2p hydrogen atoms decay?
An atom in an excited state has a 1.0% chance of emitting a photon in 0.10 ns. What is the lifetime of the excited state?
Three electrons are in a one-dimensional rigid box (i.e., an infinite potential well) of length 0.50 nm. Two are in the n = 1 state and one is in the n = 6 state. The selection rule for the rigid box allows only those transitions for which Δn is odd.a. Draw an energy-level diagram. On it, show the
The ionization energy of an atom is known to be 5.5 eV. The emission spectrum of this atom contains only the four wavelengths 310.0 nm, 354.3 nm, 826.7 nm, and 1240.0 nm. Draw an energy-level diagram with the fewest possible energy levels that agrees with these experimental data. Label each level
A sodium atom emits a photon with wavelength 818 nm shortly after being struck by an electron. What minimum speed did the electron have before the collision?
The 5d → 3p transition in the emission spectrum of sodium has a wavelength of 499 nm. What is the energy of the 5d state?
Prove that the radial probability density peaks at r = aB for the 1s state of hydrogen.
Prove that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πaB3)-1/2, as shown in Equations 41.7.
For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010 aB at distance(a) 1/2 aB,(b) aB,(c) 2 aB from the proton?
Calculate(a) The radial wave function(b) The radial probability density at r = 1/2 aB for an electron in the 1s state of hydrogen. Give your answers in terms of aB.
In LASIK surgery, a laser is used to reshape the cornea of the eye to improve vision. The laser produces extremely short pulses of light, each containing 1.0 mJ of energy.a. There are 9.7 × 1014 photons in each pulse. What is the wavelength of the laser?b. Each pulse lasts a mere 20 ns. What is
A laser emits 1.0 × 1019 photons per second from an excited state with energy E2 = 1.17 eV. The lower energy level is E1 = 0 eV.a. What is the wavelength of this laser?b. What is the power output of this laser?
A 1.0 mW helium-neon laser emits a visible laser beam with a wavelength of 633 nm. How many photons are emitted per second?
1.00 × 106 sodium atoms are excited to the 3p state at t = 0 s. At what time have 8.0 × 105 photons been emitted?
1.0 × 106 atoms are excited to an upper energy level at t = 0 s. At the end of 20 ns, 90% of these atoms have undergone a quantum jump to the ground state.a. How many photons have been emitted?b. What is the lifetime of the excited state?
An excited state of an atom has a 25 ns lifetime. What is the probability that an excited atom will emit a photon during a 0.50 ns interval?
1.0 × 106 sodium atoms are excited to the 3p state at t = 0 s. How many of these atoms remain in the 3p state at(a) T = 10 ns,(b) T = 30 ns, (c) T = 100 ns?
An electron accelerates through a 12.5 V potential difference, starting from rest, and then collides with a hydrogen atom, exciting the atom to the highest energy level allowed. List all the possible quantum-jump transitions by which the excited atom could emit a photon and the wavelength (in nm)
a. Is a 4p → 4s transition allowed in sodium? If so, what is its wavelength (in nm)? If not, why not?b. Is a 3d → 4s transition allowed in sodium? If so, what is its wavelength (in nm)? If not, why not?
What is the electron configuration of the second excited state of lithium?
Show that hc = 1240 eV nm.
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.a. 1s22s22p53sb. 1s22s22p63s23p64s23d2
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.a. 1s22s22p5b. 1s22s22p63s23p64s23d104p
Predict the ground-state electron configurations of Al, Ga, and In.
Predict the ground-state electron configurations of Mg, Sr, and Ba.
When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom with n = 1? With n = 2? With n = 3? List the quantum numbers of each state.
How many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with(a) Lithium(b) Beryllium? Explain.
A hydrogen atom has orbital angular momentum 3.65 × 10-34 J s.a. What letter (s, p, d, or f) describes the electron?b. What is the atom’s minimum possible energy? Explain.
List the quantum numbers, excluding spin, of(a) All possible 3p states(b) All possible 3d states.
In a multielectron atom, the lowest-l state for each n (2s, 3s, 4s, etc.) is significantly lower in energy than the hydrogen state having the same n. But the highest-l state for each n (2p, 3d, 4f, etc.) is very nearly equal in energy to the hydrogen state with the same n. Explain.
A neon discharge tube emits a bright reddish-orange spectrum, but a glass tube filled with neon is completely transparent. Why doesn’t the neon in the tube absorb orange and red wavelengths?
What is an atom’s ionization energy? In other words, if you know the ionization energy of an atom, what is it that you know about the atom?
What is the difference between s and S?

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