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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

Find the wavelength of the third line in the Lyman series, and identify the type of EM radiation.
Look up the values of the quantities in and verify that the Bohr radius ab is 0.529 × 10-10 m. ав h2 42 mekaz
What is a hydrogen-like atom, and how are the energies and radii of its electron orbits related to those in hydrogen?
Explain why characteristic x rays are the most energetic in the EM emission spectrum of a given element.
Verify that the ground state energy E0 is 13.6 eV by using Eo = 2n² & mek² h²
Why does the energy of characteristic x rays become increasingly greater for heavier atoms?
Observers at a safe distance from an atmospheric test of a nuclear bomb feel its heat but receive none of its copious x rays. Why is air opaque to x rays but transparent to infrared?
If a hydrogen atom has its electron in the n = 4 state, how much energy in eV is needed to ionize it?
How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.
What is the smallest-wavelength line in the Balmer series? Is it in the visible part of the spectrum?
Atomic and molecular spectra are discrete. What does discrete mean, and how are discrete spectra related to the quantization of energy and electron orbits in atoms and molecules?
Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength in the series.
Hydrogen gas can only absorb EM radiation that has an energy corresponding to a transition in the atom, just as it can only emit these discrete energies. When a spectrum is taken of the solar corona, in which a broad range of EM wavelengths are passed through very hot hydrogen gas, the absorption
Do the Balmer and Lyman series overlap? To answer this, calculate the shortest-wavelength Balmer line and the longest-wavelength Lyman line.
Lasers are used to burn and read CDs. Explain why a laser that emits blue light would be capable of burning and reading more information than one that emits infrared.
The coating on the inside of fluorescent light tubes absorbs ultraviolet light and subsequently emits visible light. An inventor claims that he is able to do the reverse process. Is the inventor’s claim possible?
A wavelength of 4.653 μm is observed in a hydrogen spectrum for a transition that ends in the nf = 5 level. What was ni for the initial level of the electron?
A singly ionized helium ion has only one electron and is denoted He+. What is the ion's radius in the ground state compared to the Bohr radius of hydrogen atom?
How can you tell that a hologram is a true threedimensional image and that those in 3-D movies are not?
A beryllium ion with a single electron (denoted Be3+) is in an excited state with radius the same as that of the ground state of hydrogen.(a) What is n for the Be3+ ion? (b) How much energy in eV is needed to ionize the ion from this excited state?
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Atoms can be ionized by thermal collisions, such as at the high temperatures found in the solar corona. One such ion is C+5, a carbon atom with only a single electron.(a) By what factor are the energies of its hydrogen- like levels greater than those of hydrogen? (b) What is the wavelength of the
The wavelength of the four Balmer series lines for hydrogen are found to be 410.3, 434.2, 486.3, and 656.5 nm. What average percentage difference is found between these wavelength numbers and those predicted by? It is amazing how well a simple formula (disconnected originally from theory) could
What is the Zeeman effect, and what type of quantization was discovered because of this effect?
Define the quantum numbers n, l, ml, s, and ms.
For a given value of n, what are the allowed values of l?The energy states of bound systems are quantized, because the particle wavelength can fit into the bounds of the system in only certain ways. This was elaborated for the hydrogen atom, for which the allowed energies are expressed as , En ∝
(a) What is the shortest-wavelength x-ray radiation that can be generated in an x-ray tube with an applied voltage of 50.0 kV? (b) Calculate the photon energy in eV. (c) Explain the relationship of the photon energy to the applied voltage.
For a given value of I, what are the allowed values of ml? What are the allowed values of ml for a given value of n? Give an example in each case.
List all the possible values of s and ms, for an electron. Are there particles for which these values are different? The same?
An x ray tube has an applied voltage of 100 kV.(a) What is the most energetic x-ray photon it can produce? Express your answer in electron volts and joules. (b) Find the wavelength of such an X–ray.
Identify the shell, subshell, and number of electrons for the following:(a) 2p3.(b) 4d9. (c) 3s1. (d) 5g16.
Figure 30.37 shows the energy-level diagram for neon.(a) Verify that the energy of the photon emitted when neon goes from its metastable state to the one immediately below is equal to 1.96 eV.(b) Show that the wavelength of this radiation is 633 nm. (c) What wavelength is emitted when the neon
The maximum characteristic x-ray photon energy comes from the capture of a free electron into a K shell vacancy. What is this photon energy in kev for tungsten, assuming the free electron has no initial kinetic energy?
Which of the following are not allowed? State which rule is violated for any that are not allowed. (a) 1p3 (b) 2p8 (c) 3g11 (d) 4f2
A helium-neon laser is pumped by electric discharge. What wavelength electromagnetic radiation would be needed to pump it? See Figure 30.37 for energy-level information.Data from figure 30.37 First Ground state 20.61 eV Helium Collision transfers energy 1.96 eV 20.66 eV Neon Metastable
Ruby lasers have chromium atoms doped in an aluminum oxide crystal. The energy level diagram for chromium in a ruby is shown in Figure 30.59. What wavelength is emitted by a ruby laser?Data from figure 30.59 Third. Second First- Ground state -3.0 eV 2.3 eV Metastable 1.79 eV 0.0 eV Ruby (Cr³+ in
If an atom has an electron in the n = 5 state with ml = 3, what are the possible values of I?
An atom has an electron with ml = 2. What is the smallest value of n for this electron?
What are the possible values of ml for an electron in the n = 4 state?
What, if any, constraints does a value of ml = 1 place on the other quantum numbers for an electron in an atom?
(a) Calculate the magnitude of the angular momentum for an l = 1 electron. (b) Compare your answer to the value Bohr proposed for the n = 1 state.
Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.
(a) How many angles can L make with the z-axis for an l = 2 electron?(b) Calculate the value of the smallest angle.
What angles can the spin of an electron make with the -axis?
(a) How many electrons can be in the n = 4 shell?(b) What are its subshells, and how many electrons can be in each?
(a) What is the minimum value of 1 for a subshell that has 11 electrons in it?(b) If this subshell is in the n = 5 shell, what is the spectroscopic notation for this atom?
(a) If one subshell of an atom has 9 electrons in it, what is the minimum value of I?(b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3 shell?
(a) List all possible sets of quantum numbers (n, l, ml, ms) for the n = 3 shell, and determine the number of electrons that can be in the shell and each of its subshells. (b) Show that the number of electrons in the shell equals 2n2 and that the number in each subshell is 2(2l + 1).
Which of the following spectroscopic notations are allowed (that is, which violate none of the rules regarding values of quantum numbers)?(a) 1s1 (b) 1d3 (c) 4s2 (d) 3p7 (e) 6h20
(a) Using the Pauli exclusion principle and the rules relating the allowed values of the quantum numbers (n, l, ml, ms), prove that the maximum number of electrons in a subshell is 2n2.(b) In a similar manner, prove that the maximum number of electrons in a shell is 2n2.
The electric and magnetic forces on an electron in the CRT in Figure 30.7 are supposed to be in opposite directions. Verify this by determining the direction of each force for the situation shown. Explain how you obtain the directions (that is, identify the rules used).Data from figure 30.7
(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0°? (b) At what angle will the fourth line of the Balmer series appear in first order?(c) At what angle will the second-order maximum be for the
A galaxy moving away from the earth has a speed of 0.0100c. What wavelength do we observe for an ni = 7 to nf = 2 transition for hydrogen in that galaxy?
In a Millikan oil-drop experiment using a setup like that in Figure 30.9, a 500-V potential difference is applied to plates separated by 2.50 cm.(a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of
What double-slit separation would produce a first- order maximum at 3.00° for 25.0-keV x rays? The small answer indicates that the wave character of x rays is best determined by having them interact with very small objects such as atoms and molecules.
Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius,
In a laboratory experiment designed to duplicate Thomson's determination of qe/me, a beam of electrons having a velocity of 6.00 × 107 m/s enters a 5.00 x 10-3 T magnetic field. The beam moves perpendicular to the field in a path having a 6.80-cm radius of curvature. Determine qe/me from these
Calculate the minimum amount of energy in joules needed to create a population inversion in a helium-neon laser containing 1.00 x 10-4 moles of neon.
A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 μm. In 1.00 ms, this laser raised the temperature of 1.00 cm3 of flesh to 100°C and evaporated it.(a) How many photons were required? You may assume flesh has the same heat of vaporization as water.(b) What
Suppose an MRI scanner uses 100-MHz radio waves.(a) Calculate the photon energy.(b) How does this compare to typical molecular binding energies?
(a) An excimer laser used for vision correction emits 193-nm UV. Calculate the photon energy in eV.(b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from
A neighboring galaxy rotates on its axis so that stars on one side move toward us as fast as 200 km/s, while those on the other side move away as fast as 200 km/s. This causes the EM radiation we receive to be Doppler shifted by velocities over the entire range of ±200 km/s. What range of
Prove that the velocity of charged particles moving along a straight path through perpendicular electric and magnetic fields is v = E/B. Thus crossed electric and magnetic fields can be used as a velocity selector independent of the charge and mass of the particle involved.
(a) What voltage must be applied to an X-ray tube to obtain 0.0100-fm-wavelength X-rays for use in exploring the details of nuclei? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm.(a) Assuming this is part of the Balmer series,
The solar corona is so hot that most atoms in it are ionized. Consider a hydrogen-like atom in the corona that has only a single electron. Construct a problem in which you calculate selected spectral energies and wavelengths of the Lyman, Balmer, or other series of this atom that could be used to
Find the energy emitted in the α decay of 239Pu.StrategyNuclear reaction energy, such as released in a decay, can be found using the equation E =(Δm)c2. We must first find Δm, the difference in mass between the parent nucleus and the products of the decay. This is easily done using masses given
(a) For carbon, calculate the energy when an electron falls from n = 3 to n = 2, then from n = 2 to n = 1. Then add these for the total energy released in the process.(b) Calculate the energy released when the electron falls directly from n = 3 to n = 1.(c) Are the energies in part a and in part b
Suppose the range for 5.0 MeV α ray is known to be 2.0 mm in a certain material. Does this mean that every 5.0 MeV α a ray that strikes this material travels 2.0 mm, or does the range have an average value with some statistical fluctuations in the distances traveled? Explain.
Find the energy emitted in the β- decay of 60Co.Strategy and ConceptAs in the preceding example, we must first find Δm, the difference in mass between the parent nucleus and the products of the decay, using masses given in Appendix A. Then the emitted energy is calculated as before, using E =
What is the difference between γ rays and characteristic x rays? Is either necessarily more energetic than the other? Which can be the most energetic?
A particle of ionizing radiation creates 4000 ion pairs in the gas inside a Geiger tube as it passes through. What minimum energy was deposited, if 30.0 eV is required to create each ion pair?
Ionizing radiation interacts with matter by scattering from electrons and nuclei in the substance. Based on the law of conservation of momentum and energy, explain why electrons tend to absorb more energy than nuclei in these interactions.
(a) Repeat the previous exercise, and convert the energy to joules or calories.(b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250-atm pressure? (The small answer is consistent with the fact that the energy
Calculate the age of the Shroud of Turin given that the amount of 14C found in it is 92% of that in living tissue.StrategyKnowing that 92% of the 14C remains means that N/N0 = 0.92. Therefore, the equation can be used to find λt. We also know that the half-life of 14C is 5730 y, and so once λt is
Calculate the activity due to 14C in 1.00 kg of carbon found in a living organism. Express the activity in units of Bq and Ci.StrategyTo find the activity R using the equation we must know N and t1/2. The half-life of 14C can be found in Appendix B, and was stated above as 5730 y. To find N, we
What characteristics of radioactivity show it to be nuclear in origin and not atomic?
It is estimated that the Chernobyl disaster released 6.0 MCi of 137Cs into the environment. Calculate the mass of 137Cs released.StrategyWe can calculate the mass released using Avogadro's number and the concept of a mole if we can first find the number of nuclei N released. Since the activity R is
Suppose a particle of ionizing radiation deposits 1.0 MeV in the gas of a Geiger tube, all of which goes to creating ion pairs. Each ion pair requires 30.0 eV of energy.(a) The applied voltage sweeps the ions out of the gas in 1.00μs. What is the current?(b) This current is smaller than the actual
Calculate the binding energy per nucleon of 4He, the α particle.StrategyTo find BE/A, we first find BE using the Equation and then divide by A. This is straightforward once we have looked up the appropriate atomic masses in Appendix A.Data from Appendix A = {[Zm(¹H)+Nmn]-m(^X)} c² $= {[Zm( H)+Nmn]-m(^X)} c$
What is the source of the energy emitted in radioactive decay? Identify an earlier conservation law, and describe how it was modified to take such processes into account.
Consider Figure 31.3. If an electric field is substituted for the magnetic field with positive charge instead of the north pole and negative charge instead of the south pole, in which directions will the α, β, and γ rays bend? N B Lead Box Phosphorescent screen (viewed from
Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, taking this to be 2.3 x 1017 kg/m3.
Explain how an α particle can have a larger range in air than a β particle with the same energy in lead.
What is the radius of an α particle?
Arrange the following according to their ability to act as radiation shields, with the best first and worst last. Explain your ordering in terms of how radiation loses its energy in matter.(a) A solid material with low density composed of low-mass atoms.(b) A gas composed of high-mass atoms.(c) A
Find the radius of a 238Pu nucleus. 238Pu is a manufactured nuclide that is used as a power source on some space probes.
Often, when people have to work around radioactive materials spills, we see them wearing white coveralls (usually a plastic material). What types of radiation (if any) do you think these suits protect the worker from, and how?
Is it possible for light emitted by a scintillator to be too low in frequency to be used in a photomultiplier tube? Explain.
The unified atomic mass unit is defined to be 1 u = 1.6605 x 10-27 kg. Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four-digit or better values for c and |qe|.
The weak and strong nuclear forces are basic to the structure of matter. Why we do not experience them directly?
What is the ratio of the velocity of a particle to that of an particle, if they have the same nonrelativistic kinetic energy?
Define and make clear distinctions between the terms neutron, nucleon, nucleus, nuclide, and neutrino.
If a 1.50-cm-thick piece of lead can absorb 90.0% of the γ rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the γ rays?
What are isotopes? Why do different isotopes of the same element have similar chemistries?
The detail observable using a probe is limited by its wavelength. Calculate the energy of a γ-ray photon that has a wavelength of 1 x 10-16 m, small enough to detect details about one-tenth the size of a nucleon. Note that a photon having this energy is difficult to produce and interacts poorly
Star Trek fans have often heard the term “antimatter drive.” Describe how you could use a magnetic field to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the
(a) Show that if you assume the average nucleus is spherical with a radius r = r0 A1/3, and with a mass of A u, then its density is independent of A.(b) Calculate that density in u/fm3 and kg/m3, and compare your results with those found in Example 31.1 for 56Fe.Data from Example 31.1(a) Find the
What conservation law requires an electron’s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.
Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern

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