(Answers to odd-numbered Conceptual Questions

Problem 93IP Referring to Example 31–3 (a) Which state has a de Broglie wavelength of 3.99 × 10?9 m? (b) What is the Bohr radius of this state?

Problem 3CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Cite one example of how the Bohr model disagrees with the quantum mechanical model of the hydrogen atom.

Problem 2CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Give a reason why the Rutherford solar-system model does not agree with experimental observations.

Problem 2P Referring to Problem 1, suppose the nucleus of the hydrogen atom were enlarged to the size of a baseball (diameter = 7.3 cm). At what typical distance from the center of the baseball would you expect to find the electron?

Problem 1P The electron in a hydrogen atom is typically found at a distance of about 5.3 × 10?11 m from the nucleus, which has a diameter of about 1.0 × 10?15 m. If you. assume the hydrogen atom to be a sphere of radius 5.3 × 10?11 m, what fraction of its volume is occupied by the nucleus?

Problem 3P Copper atoms have 29 protons in their nuclei. If the copper nucleus is a sphere with a diameter of 4.8 × 10?15 m, find the work required to bring an alpha particle (charge = +2e) from rest at infinity to the "surface" of the nucleus.

Problem 1CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Give a reason why the Thomson plum-pudding model does not agree with experimental observations.

Problem 4CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) What observation led Rutherford to propose that atoms have a small nucleus containing most of the atom's mass?

Problem 4P In Rutherford's scattering experiments, alpha particles (charge = +2e) were fired at a gold foil. Consider an alpha particle with an initial kinetic energy K heading directly for the nucleus of a gold atom (charge = +79e). The alpha particle will come to rest when all its initial kinetic energy has been converted to electrical potential energy. Find the distance of closest approach between the alpha particle and the gold nucleus for the case K = 3.0 MeV.

Problem 5CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Do you expect the light given off by (a) a neon sign or (b) an Incandescent light bulb to be continuous in distribution, or in the form of a line spectrum? Explain.

Problem 5P Find the wavelength of the Balmer series spectra! line corresponding to n = 15.

Problem 6CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) In principle, how many spectral lines are there in any given series of hydrogen? Explain.

Problem 6P What is the smallest value of n for which the wavelength of a Balmer series line is less than 400 nm?

Problem 7CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Is there an upper limit to the radius of an allowed Bohr orbit? Explain.

Problem 7P Find the wavelength of the three longest-wavelength lines of the Lyman series.

Problem 8CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) (a) Is there an upper limit to the wavelength of lines in. the spectrum of hydrogen? Explain. (b) Is there a lower limit? Explain.

Problem 8P Find the wavelength of the three longest-wavelength lines of the Paschen series.

Problem 9CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) The principal quantum number, n, can increase without limit in the hydrogen atom. Does this mean that the energy of the hydrogen atom also can increase without limit? Explain.

Problem 9P Find (a) the longest wavelength in the Lyman series and (b) the shortest wavelength in the Paschen series.

Problem 10CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) For each of the following configurations of outermost electrons, state whether the configuration is allowed by the rules of quantum mechanics. If the configuration is not allowed, give the rule or rules that are violated, (a) 2d1, (b) 1p7,(c) 3p5, (d) 4g6

Problem 10P In Table 31-1 we see that the Paschen series corresponds to n' = 3 in Equation 31-2, and that the Brackett series corresponds to n' = 4. (a) Show that the ranges of wavelengths of these two series overlap, (b) Is there a similar overlap between the Balmer series and the Paschen series? Verify your answer.

Problem 11CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) (a) In the quantum mechanical model of the hydrogen atom, there is one value of n for which the angular momentum of the electron must be zero. What is this value of n?(b) Can the angular momentum of the electron be zero in states with other values of it? Explain.

Problem 11P CE Predict/Explain (a) If the mass of the electron were magically doubled, would the ionization energy of hydrogen increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The ionization energy would increase because the increased mass would mean the electron would orbit closer to the nucleus and would require more energy to move to infinity. II. The ionization energy would decrease because a more massive electron is harder to hold in orbit, and therefore it is easier to remove the electron and leave the hydrogen ionized. III. The ionizarioii energy would be unchanged because, just like in gravitational orbits, the orbit of the electron is independent of its mass. As a result, there is no change in the energy required to move it to infinity.

Problem 12CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Would you expect characteristic X-rays to be emitted, by (a) helium atoms or (b) lithium atoms in their ground state? Explain.

Problem 12P CE Consider the Bohr model as applied to the following three atoms: (A) neutral hydrogen in the state n = 2; (B) singly ionized helium in the state n = 1; (C) doubly ionized lithium in the state n = 3. Rank these three atoms in order of increasing Bohr radius. Indicate ties where appropriate.

Problem 13CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) The elements fluorine, chlorine, and bromine are found to exhibit similar chemical properties. Explain.

Problem 13P CE Consider the Bohr model as applied to the following three atoms: (A) neutral hydrogen in the state n = 3; (B) singly ionized helium in the state n = 2; (C) doubly ionized lithium in the state n = 1. Rank these three atoms in order of increasing energy. Indicate ties where appropriate.

Problem 14P An electron in the n = 1 Bohr orbit has the kinetic energy K1. In terms of K1, what is the kinetic energy of an electron in the n = 2 Bohr orbit?

Problem 15P Find the ratio v/c for an electron in the first excited state(n = 2) of hydrogen.

Problem 16P Find the magnitude of the force exerted on an electron in the ground-state orbit of the Bohr model.

Problem 17P How much energy is required to ionize hydrogen when it is in the n = 4 state?

Problem 18P Find the energy of the photon required to excite a hydrogen atom from the n = 2 state to the n = 5 state.

Problem 19P In the Bohr model, the potential energy of a hydrogen atom in the nth orbit has a value we will call Un. What is the potential energy of a hydrogen atom when the electron is in the (n + 1)th Bohr orbit? Give your answer in terms of Un and n.

Problem 20P A hydrogen atom is in its second excited state, n = 3. Using the Bohr model of hydrogen, find (a) the linear momentum and (b) the angular momentum of the electron in this atom.

Problem 21P Referring to Problem 20, find (a) the kinetic energy of the electron, (b) the potential energy of the atom, and (c) the total energy of the atom. Give your results in eV.

Problem 23P Identify the initial and final states if an electron in hydrogen emits a photon with a wavelength of 656 mm.

Problem 22P Initially, an electron is in the n = 3 state of hydrogen. If this electron acquires an additional 1.23 eV of energy, what is the value of n in the final state of the electron?

Problem 24P IP An electron in hydrogen absorbs a photon and jump to a higher orbit, (a) Find the energy the photon must have in the initial state is n = 3 and the final state is n = 5. (b) If the initial state was n = 5 and the final state n = 7, would the energy of the photon be greater than, less than, or the same as that found in part (a)? Explain, (c) Calculate the photon energy for part (b).

Problem 25P IP Consider the following four transitions in a hydrogen atom: (i) ni = 2, nf = 6 (ii) ni = 2, nf = 8 (iii) ni = 7, nf = 8 (iv) ni = 6, nf = 2 Find (a) the longest- and (b) the shortest-wavelength photon that can be emitted or absorbed bv these transitions. Give the value of the wavelength in each case, (c) For which of these transitions does the atom lose energy? Explain.

Problem 26P IP Muoniun Muonium is a hydrogen-like atom in which the electronics replaced with a muon, a fundamental particle with a charge of — e and a mass equal to 207me. (The muon is sometimes referred to loosely as a "heavy electron.") (a) What is the Bohr radius of muonium? (b) Will the wavelengths in the Balmer series of muonium be greater than, less than, or the same as the wavelengths in the Balmer series of hydrogen? Explain, (c) Calculate the longest wavelength of the Balmer series in muonium.

Problem 27P · · IP (a) Find the radius of the n = 4 Bohr orbit of a doubly ionized lithium atom (Li2+, Z = 3). (b) Is the energy required to raise an electron from the n =4 state to the n = 5 state in Li2+ greatest than, less than, or equal to the energy required to raise an electron in hydrogen from the n = 4 state to the n = 5 state? Explain, (c) Verify your answer to part(b) by calculating the relevant energies.

Problem 28P Applying the Bohr model to a triply ionized beryllium atom (Be3+, Z = 4), find (a) the shortest wavelength of the Lyman scries for Be3+ and (b) the ionization energy required to remove the final electron in Be3+.

Problem 29P (a) Calculate the time required for an electron in the n = 2 state of hydrogen to complete one orbit about the nucleus, (b) The typical "lifetime" of an electron in the n = 2 state is roughly 10?8 s—after this time the electron is likely to have dropped back to the n = 1 stale. Estimate the number of orbits an election completes in the n = 2 state before dropping to the ground state.

Problem 30P IP The kinetic energy of an electron in a particular Bohr orbit of hydrogen is l.35 × 10?19 J. (a) Which Bohr orbit does the electron occupy? (b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the kinetic energy of the electron increase, decrease, or stay the same? Explain. (c) Calculate the kinetic energy of the electron in the orbit referred to in part (b).

Problem 31P IP The potential energy of a hydrogen atom in a particular Bohr orbit is ? 1.20 × 10?9 J. (a) Which Bohr orbit does the electron occupy in this atom? (b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the potential energy of the atom increase, decrease, or stay the same? Explain. (c) Calculate the potential energy of the atom for the orbit referred to in part (b).

Problem 32P Consider a head-on collision between two hydrogen atoms, both initially in their ground state and moving with the same speed. Find the minimum speed necessary to leave both atoms in their n = 2state after the collision.

Problem 33P A hydrogen atom is in the initial state n1 = n, where n > 1. (a) Find the frequency of the photon that is emitted when the electron jumps to state nf ? n ? 1. (b) Find the frequency of the electron's orbital motion in the state n. (c) Compare your results for parts (a) and (b) in the limit of large n.

Problem 35P Find the de Broglie wavelength of an electron in the ground state of the hydrogen atom.

Problem 34P CE Predict/Explain (a) Is the de Broglie wavelength of an electron in the n = 2 Bohr orbit of hydrogen greater than, less than, or equal to the de Broglie wavelength in the n = 1 Bohr orbit? (b) Choose the best explanation from among the following: I. The de Broglie wavelength in the nth state is 2?r/n,where r is proportional to n2. Therefore, the wavelength increases with increasing n, and is greater for n = 2 than for n = 1. II. The de Broglie wavelength of an electron in the n thstate is such that n wavelengths fit around the circumference of the orbit. Therefore, ? = 2?r/n and the wavelength for n = 2 is less than for n = 1. III. The de Broglie wavelength depends on the mass of the electron, and that is the same regardless of which state of the hydrogen atom the election occupies.

Problem 36P Find an expression for the de Broglie wavelength of an electron in the nth state of the hydrogen atom.

What is the radius of the hydrogen-atom Bohr orbit shown in Figure 31–30?

Problem 38P · · (a) Find the kinetic energy (in eV) of an electron whose de Broglie wavelength is equal to 0.5 Å, a typical atomic size, (b) Repeat part (a) for an electron with a wavelength equal to 10?15 m, a typical nuclear size.

Problem 39P What are the allowed values of ? when the principal quantum number is n = 5?

Give the value of the quantum number ?, if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of (a) \(\sqrt{6}(h / 2 \pi)\) (b) \(\sqrt{15}(h / 2 \pi)\) (c) \(\sqrt{30}(h / 2 \pi)\), or (d) \(\sqrt{36}(h / 2 \pi)\) Equation Transcription: Text Transcription: \sqrt{6}(h / 2 \pi) \sqrt{15}(h / 2 \pi) \sqrt{30}(h / 2 \pi) \sqrt{36}(h / 2 \pi)

Problem 40P How many different values of m? are possible when the principal quantum number is n = 4?

Problem 42P IP Hydrogen atom number 1is known to be in the 4/state. (a) What is the energy of this atom? (b) What is the magnitude of this atom's orbital angular momentum? (c) Hydrogen atom number 2 is in the 5d state. Ts this atom's energy greater than, less than, or the same as that of atom 1? Explain. (d) Is the magnitude of the orbital angular momentum of atom 1 greater than, less than, or the same as that of atom 2? Explain.

IP A hydrogen atom has an orbital angular momentum with a magnitude of \(10 \sqrt{57}(h / 2 \pi)\) (a) Determine the value of the quantum number \(\ell\) for this atom. (b) What is the minimum possible value of this atom's principal quantum number, Explain. (c) If \(10 \sqrt{57}(h / 2 \pi)\) is the maximum orbital angular momentum this atom can have, what is its energy? Equation Transcription: ? Text Transcription: 10 \sqrt{57}(h / 2 \pi) \ell 10 \sqrt{57}(h / 2 \pi)

Problem 44P IP The electron in a hydrogen atom with an energy of —0.544 eV is in a subshell with 18 states. (a) What is the principal quantum number, n, for this atom? (b) What is the maximum possible orbital angular momentum this atom can have? (c) Is the number of states in the subshell with the next lowest value of t equal to 16, 14, or 12? Explain.

Problem 45P IP Consider two different states of a hydrogen atom. In state I the maximum value of the magnetic quantum number is nij = 3; in state II the corresponding maximum value is tttf = 2. Let Lj and L^ represent the magnitudes of the orbital angular momentum of an electron in states T and II, respec-. tively. (a) Is Lj greater than, less than, or equal to Ljf? Explain. (b) Calculate the ratio Lj/Ln.

Problem 46P CE How many electrons can occupy (a) the 2p subshell and (b) the 3p subshell?

Problem 47P CE (a) How many electrons can occupy the 3d subshell? (b) How many electrons can occupy the n = 2shell?

The electronic configuration of a given atom is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1}\). How many electrons are in this atom? Equation Transcription: Text Transcription: 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1}

Problem 49P Give the electronic configuration for the ground state of carbon.

Problem 50P List the values of the four quantum numbers (n, ?, m?, ms)for each of the electrons in the ground state of neon.

Problem 51P Give the electronic configuration for the ground state of nitrogen.

Problem 52P Give a list of all possible sets of the four quantum numbers (n, ?, m?, ms) for electrons in the 3s subshell.

Problem 53P Give a list of all possible sets of the four quantum numbers (n, ?, m?, ms) for electrons in the 3p subshell.

Problem 54P List the values of the four quantum numbers (n, ?, m?, ms) for each of the electrons in the ground state of magnesium.

Problem 55P The configuration of the outer electrons in Ni is 3d8 4s2. Write out the complete electronic configuration for Ni.

Problem 56P Determine the number of different sets of quantum numbers possible for each of the following shells: (a) n = 2, (b) n = 3, (c) n = 4.

Problem 58P Suppose that the 5d subshell is filled in a certain atom. Write out the 10 sets of four quantum numbers (n, l, ml, ms)for the electrons in this subshell.

Problem 57P Generalize the results of Problem 56 and show that the number of different sets of quantum numbers for the n thshell is 2n2.

Problem 59P CE Predict/Explain (a) Tn an X-ray tube, do you expect the wavelength of the characteristic X-rays to increase, decrease, or stay the same if the energy of the electrons striking the target is increased? (b) Choose the list explanation from among the following: I. Increasing the energy of the incoming electrons will increase the wavelength of the emitted X-rays. II. When the energy of the incoming electrons is increased, the energy of the X-rays is also increased; this, in turn, decreases the wavelength. III. The wavelength of characteristic X-rays depends only on the material used in the metal target, and does not change if the energy of incoming electrons is increased.

Problem 60P CE Is the wavelength of the radiation that excites a fluorescent material greater than, less than, or equal to the wavelength of the radiation the material emits? Explain.

Problem 61P Using the Bohr model, estimate the wavelength of the K? X-ray in nickel (Z = 28).

Problem 62P Using the Bohr model, estimate the energy of a K? X-ray emitted by lead (Z = 82).

Problem 63P The K-shell ionization energy of iron is 8500 eV, and its L-shell ionization energy is 2125 eV. What is the wavelength of K? X-rays emitted by iron?

Problem 64P An electron drops from the L shell to the K shell and gives off an X-ray with a wavelength of 0.0205 nm. What is the atomic number of this atom?

Problem 65P Consider an X-ray tube that uses platinum (Z = 78) as its target, (a) Use the Bohr model to estimate the minimum kinetic energy electrons must have in order for K? X-rays to just appear in the X-ray spectrum of the tube, (b) Assuming the electrons are accelerated from rest through a voltage V, estimate the minimum voltage necessary to produce the KB X-rays.

Problem 66P BIO Photorefractive Keratectomy A person's vision may be improved significantly by having the cornea reshaped with a laser beam, in a procedure known as photo refractive keratectomy. The excimer laser used in these treatments produces ultraviolet light with a. wavelength of 193 nm. (a) What is the difference in energy between the two levels that participate in stimulated emission in the excimer laser? (b) How many photons from this laser are required to deliver an energy of 1.58 × 10?13 J to the cornea?

Problem 67GP Consider the following three transitions in a hydrogen atom: (A) ni = 5, nf = 2; (B) ni = 7, nf = 2; (C) ni = 7, nf = 6. Rank the transitions in order of increasing (a) wavelength and (b) frequency of the emitted photon. Indicate ties where appropriate.

Problem 68GP Suppose an electron is in the ground state of hydrogen. (a) What is the highest-energy photon this system can absorb without dissociating the electron from the proton? Explain. (b) What is the lowest-energy photon this system can absorb? Explain.

Problem 69GP The electronic configuration of a particular carbon atom is 1s22s22p13s1. Is this atom in its ground state or in an excited state? Explain.

Problem 70GP The electronic configuration of a particular potassium atom is 1s22s22p63s23p63d1. Is this atom in its ground state or in an excited state? Explain.

Problem 71GP Do you expect the ionization energy of sodium (Na) to be greater than, less than, or equal to the ionization energy of lithium (Li)? Explain.

Problem 72GP Find the minimum frequency a photon must have it it is to ionize the ground state of the hydrogen atom.

It was pointed out in Section that intermolecular collisions at room temperature do not have enough energy to cause an excitation in hydrogen from the \(n=1\) state to the \(n=2\) state. Given that the average kinetic energy of a hydrogen atom in a high-temperature gas is \(\frac{3}{2} k T\) (where is Boltzmann's constant), find the minimum temperature required for atoms to have enough thermal energy to excite electrons from the ground state to the\(n=2\) state. Equation Transcription: Text Transcription: n=1 n=2 \frac{3}{2} k T n=2

The electron in a hydrogen atom makes a transition from the \(n=4\) state to the \(n=2\) state, as indicated in Figure . (a) Determine the linear momentum of the photon emitted as a result of this transition. (b) Using your result to part (a), find the recoil speed of the hydrogen atom, assuming it was at rest before the photon was emitted. Equation Transcription: Text Transcription: n=4 n=2

Referring to Problem 74, find (a) the energy of the emitted photon and (b) the kinetic energy of the hydrogen atom after the photon is emitted. (c) Do you expect the sum of the energies in parts (a) and (b) to be greater than, less than, or the same as the difference in energy between the \(n=4 \text { and } n=1\) and states of hydrogen? Explain. Equation Transcription: Text Transcription: n=4 and n=1

Problem 76GP BIO Laser Eye Surgery In laser eye surgery, the laser emits a 1.45-ns pulse focused on a spot that is 34.0 ? m in diameter, (a) If the energy contained in the pulse is 2.75 mJ, what is the power per square meter (the irradiance) associated with this beam? (b) Suppose a molecule with a diameter of 0.650 nm is irradiated by the laser beam. How much energy does the molecule receive in one pulse from the laser? (The energy obtained in part (b) is more than enough to dissociate a molecule.)

Problem 77GP Consider an electron in the ground-state orbit of the Bohr model of hydrogen. (a) Tind the time required for the electron to complete one orbit about the nucleus. (b) Calculate the current (in amperes) corresponding to the electron's motion.

Problem 78GP A particular Bohr orbit in a hydrogen atom has a total energy of —0.85 eV. What are (a) the kinetic energy of the electron in this orbit and (b) the electric potential energy of the system?

Problem 79GP The element helium is named for the Sun because that is where it was first observed. (a) What is the shortest wavelength that one would expect to observe from a singly ionized helium atom in the atmosphere of the Sun? (b) Suppose light with a wavelength of 388.9 nm is observed from singly ionized helium. What are the initial and final values of the quantum number n corresponding to this wavelength?

Problem 80GP An ionized atom has only a single electron. The n = 6 Bohr orbit of this electron has a radios of 2.72 x 10?10 m. Find (a) the atomic number Z of this atom and (b) the total energy E of its n = 3 Bohr orbit.

Problem 81GP Find the approximate wavelength of K? X-rays emitted by molybdenum (Z = 42), and compare your result with Figure 31–22. (Hint: An electron in the M shell is shielded from the nucleus by the single electron in the K shell, plus all the electrons in the L shell.)

Problem 82GP Referring to the hint given in Problem, estimate the wave- ' length of La X-rays in molybdenum.

IP The Pickering Series In 1896, the American astronomer Edward C. Pickering (1846-1919) discovered an unusual series of spectral lines in light from the hot star Zeta Puppis. After some time, it was determined that these lines are produced by singly ionized helium. In fact, the "Pickering series" is produced when electrons drop from higher levels to the \(n=4\) level of \(H e^{+}\). Spectral lines in the Pickering series have wavelengths given by \(\frac{1}{\lambda}=C\left(\frac{1}{16}-\frac{1}{n^{2}}\right)\) In this expression, \(n=5,6,7, \ldots\) (a) Do you expect the constant to be greater than, less than, or equal to the Rydberg constant Explain. (b) Find the numerical value of (c) Pickering lines with \(n=6,8,10, \ldots\) correspond to Balmer lines in hydrogen with \(n=3,4,5,, \ldots\) Verify this assertion for the \(n=6\) Pickering line. Equation Transcription: Text Transcription: n=4 He+ 1 over \lambda=C (116-1n2) n=5,6,7,... n=6,8,10,... n=3,4,5,,... n=6

Problem 84GP IP Rydberg Atoms There is no limit to the size a hydrogen atom can attain, provided it is free from disruptive outside influences. In fact, radio astronomers have detected radiation from large, so-called "Rydberg atoms" in the diffuse hydrogen gas of interstellar space. (a) Find the smallest value of n such that the Bohr radius of a single hydrogen atom is greater than 8.0 microns, the size of a typical single-celled organism. (b) Find the wavelength of radiation this atom emits when its electron drops from level n to level n ?1. (c) If the electron drops one more level, from n ? 1 to n ? 2,is the emitted wavelength greater than or less than the value found in part (b)? Explain.

Consider a particle of mass charge , and constant speed moving perpendicular to a uniform magnetic field of magnitude , as shown in Figure . The particle follows a circular path. Suppose the angular momentum of the particle about the center of its circular motion is quantized in the following way: \(\mathrm{mvr}=n \hbar\), where \(n=1,2,3, \ldots\), and \(\hbar=h / 2 \pi\) a. Show that the radii of its allowed orbits have the following values: \(r_{n}=\sqrt{\frac{n \hbar}{q B}}\) b. Find the speed of the particle in each allowed orbit. Equation Transcription: Text Transcription: mvr=n \hbar n=1,2,3, \ldots \hbar=h / 2 \pi r_n=\sqrt{\frac{n \hbar q B

Consider a particle of mass \(m\) confined in a one-dimensional box of length \(L\) In addition, suppose the matter wave associated with this particle is analogous to a wave on a string of length \(L\) that is fixed at both ends. Using the de Broglie relationship, show that (a) the quantized values of the linear momentum of the particle are \(P_{n}=\frac{n h}{2 L} \quad n=1,2,3, \ldots\) and (b) the allowed energies of the particle are \(E_{n}=n^{2}\left(\frac{h^{2}}{8 m L^{2}}\right) \quad n=1,2,3, \ldots\) Equation Transcription: Text Transcription: m L L P_n = frac{n h}{2 L} n = 1,2,3, … E_n = n^{2}(frac{h^{2}}{8 m L^{2}}) n = 1,2,3, ...

Show the time required for an electron in the \(n\)th Bohr orbit of hydrogen to circle the nucleus once is given by \(T=T_{1} n^{3} \quad n=1,2,3, \ldots\) where \(T_{1}=h^{3} / 4 \pi^{2} m k^{2} e^{4}\) Equation Transcription: Text Transcription: n T = T_{1} n^{3} n = 1,2,3, … T_1 = h^{3} / 4pi^{2} mk^{2} e^{4}

Problem 88PP Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts? A. 1.49 W B. 5.76 W C. 5.92 W D. 6.07 W

Problem 89PP A different type of laser also emits 1.49 × 1019 photons per second. If all of its photons have a wavelength of 414.0 nm, is its power output greater than, less than, or equal to the power output of the argon laser in Problem? Problem 88. Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts? A. 1.49 W B. 5.76 W C. 5.92 W D. 6.07 W

Problem 90PP What is the power output of the laser in Problem? A. 1.23 W B. 2.39 W C. 4.80 W D. 7.16 W Problem 89. · · A different type of laser also emits 1.49 × 1019 photons per second. If all of its photons have a wavelength of 414.0 nm, is its power output greater than, less than, or equal to the power output of the argon laser in Problem? Problem 88. Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts? A. 1.49 W B. 5.76 W C. 5.92 W D. 6.07 W

Problem 91PP What is the energy difference (in eV) between the states of an argon atom that are responsible for a photon with a wavelength of 514.5 nm? A. 2.13 eV B. 2.42 eV C. 3.87 eV D. 6.40 eV

Problem 92IP IP Referring to Example 31–3 Suppose the electron is in a state whose standing wave consisting of two wavelengths. (a) Is the wavelength of this standing wave greater than or less than 1.33 × 10?9 m? (b) Find the wavelength of this standing wave.