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college physics reasoning

Questions and Answers of College Physics Reasoning

How many electrons, protons, and neutrons are contained in the following atoms or ions:(a) \({ }^{9} \mathrm{Be}^{+}\),(b) \({ }^{12} \mathrm{C}\), and(c) \({ }^{15} \mathrm{~N}^{+++}\)?
What is the quantum number of this hydrogen atom?
Write the symbol for an atom or ion with:a. four electrons, four protons, and five neutrons.b. six electrons, seven protons, and eight neutrons.
What are the quantum numbers n and l for a hydrogen atom with E (13.60/9) eV and L = V2h?
The \(n=3\) state of hydrogen has \(E_{3}=-1.51 \mathrm{eV}\).a. Why is the energy negative?b. What is the physical significance of the specific number \(1.51 \mathrm{eV}\) ?
Which element has the ground-state electron configurationA. P B. A1 C. B D. Ge 1s2s22p63s3p?
Figure P29.8 is an energylevel diagram for a simple atom. What wavelengths appear in the atom's(a) emission spectrum and(b) absorption spectrum?An electron with \(2.0 \mathrm{eV}\) of \(n=3
In this hypothetical atom, what is the photon energy £photon of the longest wavelength photons emitted by atoms in the 5p state?A. 1.0 eV B. 2.0eV C. 3.0 eV D. 4.0eV Energy (eV) S 5- 4 3- 2- 5s -5p
What are the \(n\) and \(l\) values of the following states of a hydrogen atom:(a) \(4 d\),(b) \(5 f\),(c) \(6 s\) ?
How would you label the hydrogen-atom states with the following \((n, l, m)\) quantum numbers:(a) \((4,3,0)\),(b) \((3,2,1)\),(c) \((3,2,-1)\) ?
A hydrogen atom is in a state with principal quantum number \(n=5\). What possible values of the orbital quantum number \(l\) could this atom have?
The allowed energies of a simple atom are \(0.0 \mathrm{eV}, 4.0 \mathrm{eV}\), and \(6.0 \mathrm{eV}\). An electron traveling at a speed of \(1.6 \times 10^{6} \mathrm{~m} / \mathrm{s}\)
In a multielectron atom, does a \(5 s\) electron have higher or lower energy than a \(4 f\) electron? Explain.
Do the following electron configurations represent a possible state of an element? If so, (i) identify the element and (ii) determine if this is the ground state or an excited state. If not, why
Why is the section of the periodic table labeled as "transition elements" exactly 10 elements wide in all rows?
Infrared light with a wavelength of \(1870 \mathrm{~nm}\) is emitted from hydrogen. What are the quantum numbers of the two states involved in the transition that emits this light?
a. Which states of a hydrogen atom can be excited by a collision with an electron with kinetic energy \(K=12.5 \mathrm{eV}\) ? Explain.b. After the collision the atom is not in its ground state. What
A hydrogen atom is excited from its ground state to the \(n=\) 4 state. The atom subsequently emits three photons, one of which has a wavelength of \(656 \mathrm{~nm}\). What are the wavelengths of
Figure Q29.20 shows the energy \(\quad E(\mathrm{eV})\) levels of a hypothetical atom. \(\quad(n+1) p\)a. What minimum kinetic energy (in \(\mathrm{eV}\) ) must an electron have to collisionally
A 2.0 eV photon is incident on an atom in the \(p\) stat shown in the energy-level diagram in Figure Q29.22. Does the atom undergo an absorption transition, a stimulated emission transition, or
The energy of a hydrogen atom is \(12.09 \mathrm{eV}\) above its ground-state energy. As a multiple of \(\hbar\), what is the largest angular momentum that this atom could have?
An electron collides with an atom in its ground state. The atom then emits a photon of energy \(E_{\text {photon }}\). In this process the change \(\Delta E_{\text {elec }}\) in the electron's energy
How many states are in the \(l=4\) subshell?A. 8 B. 9 C. 16 D. 18 E. 22
The angular momentum of a hydrogen atom is \(4.70 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\). What is the minimum energy, in \(\mathrm{eV}\), that this atom could have?
What is the ground-state electron configuration of calcium \((Z=20)\) ?A. \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{8}\)B. \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} 4 p^{1}\)C. \(1 s^{2} 2 s^{2}
The energy of a hydrogen atom is \(-3.40 \mathrm{eV}\). What is the electron's kinetic energy?A. \(1.70 \mathrm{eV}\)B. \(2.62 \mathrm{eV}\)C. \(3.40 \mathrm{eV}\)\(\begin{array}{ll}\text { D. } 5.73
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.a. \(1 s^{2} 2 s^{2} 2 p^{5}\)b. \(1 s^{2} 2 s^{2} 2
a. With what element is the \(3 s\) subshell first completely filled?b. With what element is the \(5 d\) subshell first half filled?
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.a. \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}
A "soft x-ray" photon with an energy of \(41.8 \mathrm{eV}\) is absorbed by a hydrogen atom in its ground state, knocking the atom's electron out. What is the speed of the electron as it leaves the
Explain what is wrong with these electron configurations:a. \(1 s^{2} 2 s^{2} 2 p^{8} 3 s^{2} 3 p^{4}\)b. \(1 s^{2} 2 s^{3} 2 p^{4}\)
Hydrogen gas absorbs light of wavelength \(103 \mathrm{~nm}\). Afterward, what wavelengths are seen in the emission spectrum?
a. Is a \(4 p \rightarrow 4 s\) transition allowed in sodium? If so, what is its wavelength? If not, why not?b. Is a \(3 d \rightarrow 4 s\) transition allowed in sodium? If so, what is its
Figure P29.38 shows a molecular energy-level diagram. What are the longest and shortest wavelengths in(a) the molecule's absorption spectrum and(b) the molecule's fluorescence spectrum?Figure P29.38
In LASIK surgery, a laser is used to reshape the cornea of the eye to improve vision. The laser produces extremely short\(\mathbb{N T}\) pulses of light, each containing \(1.0 \mathrm{~mJ}\) of
Two of the wavelengths emitted by a hydrogen atom are \(102.6 \mathrm{~nm}\) and \(1876 \mathrm{~nm}\).a. What are the Balmer formula \(n\) and \(m\) values for each of these wavelengths?b. For each
In Example 29.2 it was assumed that the initially stationary gold nucleus would remain motionless during a head-on collision with an \(8.3 \mathrm{MeV}\) alpha particle. What is the actual recoil
Consider the gold isotope \({ }^{197} \mathrm{Au}\).a. How many electrons, protons, and neutrons are in a neutral \({ }^{197} \mathrm{Au}\) atom?b. The gold nucleus has a diameter of \(14.0
The diameter of an atom is \(1.2 \times 10^{-10} \mathrm{~m}\) and the diameter of its nucleus is \(1.0 \times 10^{-14} \mathrm{~m}\). What percent of the atom's volume is occupied by mass and what
If the nucleus is a few \(\mathrm{fm}\) in diameter, the distance between the centers of two protons must be \(\approx 2 \mathrm{fm}\).a. Calculate the repulsive electric force between two protons
A hydrogen atom in the ground state absorbs a \(12.75 \mathrm{eV}\) photon. Immediately after the absorption, the atom undergoes a quantum jump to the next-lowest energy level. What is the wavelength
Potassium atom 1 , with a mass of \(6.47 \times 10^{-26} \mathrm{~kg}\), has a speed of \(1.30 \times 10^{4} \mathrm{~m} / \mathrm{s}\). It collides with potassium atom 2 that is at rest, exciting
a. Calculate the orbital radius and the speed of an electron in both the \(n=99\) and the \(n=100\) states of hydrogen.b. Determine the orbital frequency of the electron in each of these states.c.
A particular emission line in the hydrogen spectrum has a wavelength of \(656.5 \mathrm{~nm}\). What are all possible transitions (e.g., \(6 d \rightarrow 2 s\) ) that could give rise to this
Germicidal lamps are used to sterilize tools in biological and medical facilities. One type of germicidal lamp is a low-pressure mercury discharge tube, similar to a fluorescent lightbulb, that has
Fluorescence microscopy, is an important tool in modern cell biology. A variation on this technique depends on a phenomenon known as two-photon excitation. If two photons are absorbed simultaneously
An LED emits green light. Increasing the size of the band gap could change the color of the emitted light to A. Red C. Yellow B. Orange D. Blue Light-emitting diodes, known by the acronym LED,
Suppose the LED band gap is \(2.5 \mathrm{eV}\), which corresponds to a wavelength of \(500 \mathrm{~nm}\). Consider the possible electron transitions in Figure P29.76. \(500 \mathrm{~nm}\) is theA.
The same kind of semiconducting material used to make an LED can also be used to convert absorbed light into electrical energy, essentially operating as an LED in reverse. In this case, the
The efficiency of a light source is the percentage of its energy input that gets radiated as visible light. If some of the blue light in an LED is used to cause a fluorescent material to glow,A. The
How many protons and how many neutrons are in(a) \({ }^{3} \mathrm{H}\),(b) \({ }^{40} \mathrm{Ar}\),(c) \({ }^{40} \mathrm{Ca}\), and(d) \({ }^{239} \mathrm{Pu}\) ?
This energy-level diagram represents an atom with four electrons. What element is this? And is this the ground state of the atom or an excited state?A. Lithium, ground state B. Lithium, excited state
Given that \(m_{\mathrm{H}}=1.007825 \mathrm{u}\), is the mass of a hydrogen atom \({ }^{1} \mathrm{H}\) greater than, less than, or equal to \(1 / 12\) the mass of \(\mathrm{a}^{12} \mathrm{C}\)
How many protons and how many neutrons are in(a) \({ }^{3} \mathrm{He}\),(b) \({ }^{20} \mathrm{Ne}\),(c) \({ }^{60} \mathrm{Co}\), and(d) \({ }^{226} \mathrm{Ra}\) ?
Three electrons orbit a neutral 6Li atom. How many electrons orbit a neutral 7Li atom?
a. Is there a stable \({ }_{3}^{30} \mathrm{Li}\) nucleus? Explain how you made your determination.b. Is there a stable \({ }_{92}^{184} \mathrm{U}\) nucleus? Explain how you made your determination.
Use the data in Appendix D to calculate the chemical atomic mass of lithium, to two decimal places.Appendix D Atomic and Nuclear Data Mass Element Symbol Number (A) (Neutron) n H 1 D 2 T 3 3 4 6 3
238U is long-lived but ultimately unstable; it will eventually spontaneously break into two fragments, a 4He nucleus and a 234Th nucleus, in a process called alpha decay, which we'll learn about in
Use the data in Appendix D to calculate the chemical atomic mass of neon, to two decimal places.Appendix D Atomic and Nuclear Data Mass Element Symbol Number (A) (Neutron) n H 1 D 2 T 3 3 4 6 3
Rounding slightly, the nucleus \({ }^{3} \mathrm{He}\) has a binding energy of \(2.5 \mathrm{MeV} /\) nucleon and the nucleus \({ }^{6} \mathrm{Li}\) has a binding energy of \(5 \mathrm{MeV} /\)
Based on the model of nuclear energy levels and transitions you have seen, would you expect 13C to be stable?
What are the energy equivalents (in \(\mathrm{MeV}\) ) of the mass of(a) an electron,(b) a proton,(c) a hydrogen atom, and(d) a helium atom?
The cobalt isotope 60Co (Z = 27) decays to the nickel isotope 60Ni (Z = 28). The decay process is A. Alpha decay.B. Beta-minus decay.C. Beta-plus decay.D. Gamma decay.
The chemical atomic mass of hydrogen, with the two stable isotopes \({ }^{1} \mathrm{H}\) and \({ }^{2} \mathrm{H}\) (deuterium), is \(1.00798 \mathrm{u}\). Use this value to determine the natural
Nucleus A decays to nucleus B, with a half-life of 10 minutes.A pure sample of nucleus A contains 24,000 particles. Using what you've learned in Figure 30.16, after 30 minutes the sample will contain
A sample of 1000 radioactive atoms has a 10 minute half-life.How old is the sample when 750 atoms have decayed?A. 10 minutes B. 15 minutes C. 20 minutes D. 30 minutes
Calculate (in \(\mathrm{MeV}\) ) the total binding energy and the binding energy per nucleon(a) for \({ }^{40} \mathrm{Ar}\) and(b) for \({ }^{40} \mathrm{~K}\).
A patient ingests a radioactive isotope to treat a tumor. The isotope provides a dose of 0. 10 Gy. Which type of radiation will give the highest dose equivalent in Sv?A. Alpha particles B. Beta
A radioactive sample's half-life is \(1.0 \mathrm{~min}\), so each nucleus in the sample has a \(50 \%\) chance of undergoing a decay sometime between \(t=0\) and \(t=1 \mathrm{~min}\). One
Calculate (in \(\mathrm{MeV}\) ) the binding energy per nucleon for \({ }^{12} \mathrm{C}\) and \({ }^{13} \mathrm{C}\). Which is more tightly bound?
The material that formed the earth was created in a supernova explosion approximately 6 billion years ago. The two most common isotopes of uranium, \({ }^{238} \mathrm{U}\) and \({ }^{235}
Calculate (in \(\mathrm{MeV}\) ) the binding energy per nucleon for(a) \({ }^{14} \mathrm{~N}\),(b) \({ }^{56} \mathrm{Fe}\), and(c) \({ }^{207} \mathrm{~Pb}\).
An investigator receives a sample of a short-lived isotope that was created using a cyclotron. Explain why it is not possible to tell the age of an individual nucleus, but it is possible to determine
When a nucleus of \({ }^{235} \mathrm{U}\) undergoes fission, it breaks into two smaller, more tightly bound fragments. Calculate the binding energy per nucleon for \({ }^{235} \mathrm{U}\) and for
When a nucleus of \({ }^{240} \mathrm{Pu}\) undergoes fission, it breaks into two smaller, more tightly bound fragments. Calculate the binding energy per nucleon for \({ }^{240} \mathrm{Pu}\) and for
Radiocarbon dating assumes that the abundance of \({ }^{14} \mathrm{C}\) in the environment has been constant. Suppose \({ }^{14} \mathrm{C}\) was less abundant 10,000 years ago than it is today.
a. Compute the binding energy of the reactants and of the products in the nuclear fusion reactionb. What is the change in binding energy per nucleon in this reaction? 2H+LiHe++He
Draw an energy-level diagram, similar to Figure 30.9, for the protons and neutrons in \({ }^{11} \mathrm{Be}\). Do you expect this nucleus to be stable? FIGURE 30.9 Nuclear energy-level diagrams of
Identify the unknown \(\mathrm{X}\) in the following decays:a. \({ }_{86}^{222} \mathrm{Rn} \rightarrow{ }_{84}^{218} \mathrm{Po}+\mathrm{X}\)b. \({ }_{88}^{228} \mathrm{Ra} \rightarrow{ }_{89}^{228}
Are the following decays possible? If not, why not?a. \({ }_{90}^{232} \mathrm{Th} \rightarrow{ }_{92}^{236} \mathrm{U}+\alpha\)b. \({ }_{94}^{238} \mathrm{Pu} \rightarrow{ }_{92}^{236}
The nuclei of \({ }^{4} \mathrm{He}\) and \({ }^{16} \mathrm{O}\) are very stable and are often referred to as "doubly magic" nuclei. Use what you know about energy levels to explain what is special
You have seen that filled electron energy levels correspond to chemically stable atoms. A similar principle holds for nuclear energy levels; nuclei with equally filled proton and neutron energy
\({ }^{15} \mathrm{O}\) and \({ }^{131} \mathrm{I}\) are isotopes used in medical imaging. \({ }^{15} \mathrm{O}\) is a BIO beta-plus emitter, \({ }^{131}\) I a beta-minus emitter. What are the
Spacecraft have been powered with energy from the alpha decay of \({ }^{238} \mathrm{Pu}\). What is the daughter nucleus?
Identify the unknown isotope \(\mathrm{X}\) in the following decays.a. \({ }^{234} \mathrm{U} \rightarrow \mathrm{X}+\alpha\)b. \({ }^{32} \mathrm{P} \rightarrow \mathrm{X}+\mathrm{e}^{-}\)c.
Identify the unknown isotope \(\mathrm{X}\) in the following decays.a. \(\mathrm{X} \rightarrow{ }^{224} \mathrm{Ra}+\alpha\)b. \(\mathrm{X} \rightarrow{ }^{207} \mathrm{~Pb}+\mathrm{e}^{-}\)c. \({
What is the energy (in \(\mathrm{MeV}\) ) released in the alpha decay of \({ }^{228} \mathrm{Th}\) ?
Medical gamma imaging is generally done with the technetium isotope \({ }^{99} \mathrm{Tc}^{*}\), which decays by emitting a gammaray photon with energy \(140 \mathrm{keV}\). What is the mass loss of
Cobalt has one stable isotope, \({ }^{59} \mathrm{Co}\). What are the likely decay modes and daughter nuclei for(a) \({ }^{56} \mathrm{Co}\) and(b) \({ }^{62} \mathrm{Co}\) ?
Give a description of the electron capture process in terms of quarks.The following two questions concern an uncommon nuclear decay mode known as electron capture. Certain nuclei that are proton-rich
Manganese has one stable isotope, \({ }^{55} \mathrm{Mn}\). What are the likely decay modes and daughter nuclei for(a) \({ }^{51} \mathrm{Mn}\) and(b) \({ }^{59} \mathrm{Mn}\) ?
Electron capture is usually followed by the emission of an \(\mathrm{x}\) ray. Why?The following two questions concern an uncommon nuclear decay mode known as electron capture. Certain nuclei that
The radioactive hydrogen isotope \({ }^{3} \mathrm{H}\) is called tritium. It decays by beta-minus decay with a half-life of 12.3 years.a. What is the daughter nucleus of tritium?b. A watch uses the
\({ }^{74} \mathrm{As}\) is a beta-plus emitter used for locating tumors with PET. What is the daughter nucleus?A. \({ }_{33}^{73} \mathrm{As}\)B. \({ }_{32}^{74} \mathrm{Ge}\)C. \({ }_{34}^{74}
The barium isotope \({ }^{133} \mathrm{Ba}\) has a half-life of 10.5 years. A sample begins with \(1.0 \times 10^{10}{ }^{133} \mathrm{Ba}\) atoms. How many are left after(a) 2 years,(b) 20 years,
When uranium fissions, the fission products are radioactive because the nuclei are neutron-rich. What is the most likely decay mode for these nuclei?A. Alpha decay C. Beta-plus decay B. Beta-minus
The cadmium isotope \({ }^{109} \mathrm{Cd}\) has a half-life of 462 days. A sample begins with \(1.0 \times 10^{12}{ }^{109} \mathrm{Cd}\) atoms. How many are left after(a) 50 days,(b) 500 days,
What is the unknown isotope in the following fission reaction: \(\mathrm{n}+{ }^{235} \mathrm{U} \rightarrow{ }^{131} \mathrm{I}+\) ? + \(3 \mathrm{n}\)A. \({ }^{86} \mathrm{Rb}\)B. \({ }^{102}
The Chernobyl reactor accident in what is now Ukraine was the worst nuclear disaster of all time. Fission products from the reactor core spread over a wide area. The primary radiation exposure to
An investigator has \(0.010 \mu \mathrm{g}\) samples of two isotopes of strontium, \({ }^{89} \mathrm{Sr}\left(t_{1 / 2}=51\right.\) days \()\) and \({ }^{90} \mathrm{Sr}\left(t_{1 / 2}=28\right.\)

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