Mastering Physics Solutions Chapter 31 Atomic Physics
Chapter 31 Atomic Physics Q.1CQ
Give areason why the Thomson plum-pudding model does not agree with experimental observations.
Solution:
Experimental observations that Thomson plum – pudding model does not agree.
1) Thomson observed only one spectral line by his assumption while experimental observation reveals that hydrogen spectrum consists of five different series with several lines in each series.
2) This model could not provide any satisfactory mechanism for explaining the large deflection suffered by – particles in Rather-ford’s experiment.
Chapter 31 Atomic Physics Q.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 hydrogenatom to be a sphere of radius 5.3 × 10−11 m, what fraction of its volume is occupied by the nucleus?
Solution:
Chapter 31 Atomic Physics Q.2CQ
Give a reason why the Rutherford solar-system model does not agree with experimental observations.
Solution:
According to Rutherford atomic model, electrons revolve round the nucleus in circular orbits. Such a revolving electron will lose its energy continuously and it falls into the nucleus after a certain instant of time. Therefore, the atom gets collapsed. This is in contradiction with the practical observations which shows atoms are stable. Due to this reason Rutherford solar system model does not agree with experimental observation.
Chapter 31 Atomic Physics Q.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?
Solution:
Chapter 31 Atomic Physics Q.3CQ
Cite one example of how the Bohr model disagrees with the quantum mechanical model of the hydrogen atom.
Solution:
According to Bohr’s theory we have only energy level for an electron. When there are some electrons in a state ‘n’ then all these electrons are equidistant from the centre of the atom.
But in quantum theory, we have sub levels and sub – sub levels of an electron. So the electrons need not to be equidistant from the centre of the atom even though they are in the same state ‘n’. This is one example out of several that Bohr model disagrees with the quantum mechanical model of hydrogen atoms.
Chapter 31 Atomic Physics Q.3P
Copper atoms have 29 protons in their nuclei. If the coppernucleus 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.
Solution:
Chapter 31 Atomic Physics Q.4CQ
What observation led Rutherford to propose that atoms have a small nucleus containing most of the atom’s mass?
Solution:
When conducting the experiment of α-particle scattering, surprisingly he observed few particles turned back towards source itself. This result led to the idea that there must be a great concentration of positive charge and mass within an atom.
Chapter 31 Atomic Physics Q.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 initialkinetic energy has been converted to electrical potential energy. Find the distance of closest approachbetween the alpha particle and the gold nucleus for the case K = 3.0 MeV.
Solution:
Chapter 31 Atomic Physics Q.5CQ
Do yon expect the light given off by (a) a neon sign or (b) an Incandescent lightbulb to be continuous in distribution, or in the form of a line spectrum? Explain.
Solution:
a) A neon sign is obtained when neon gas under a low pressure is applied with high voltage. As the glass tube of a neon sign contains a low – pressure gas we expect that the light from the sign to be in the form of a line spectrum.
b) But in incandescent bulb the light is emitted by the burning of the filament. Therefore the radiation is the black body radiation from a hot object. Therefore, its radiation is distributed as a continuous distribution.
Chapter 31 Atomic Physics Q.5P
Find the wavelength of the Balmer series spectra! line corresponding to n = 15.
Solution:
Chapter 31 Atomic Physics Q.6CQ
In principle, how many spectral lines are there inany given series of hydrogen? Explain.
Solution:
Chapter 31 Atomic Physics Q.6P
What is the smallest value of n for which the wavelength of a Balmer scries line is less than 400 mm?
Solution:
Chapter 31 Atomic Physics Q.7CQ
Is there an upper limit to the radius of an allowed Bohr orbit? Explain.
Solution:
Chapter 31 Atomic Physics Q.7P
Find the wavelength of the three longest-wavelength lines of the Lyman series.
Solution:
Chapter 31 Atomic Physics Q.8CQ
(a) Is there an upper limit to the wavelength of lines in. the spectrum of hydrogen? Explain. (b) Is there a lower limit? Explain.
Solution:
Chapter 31 Atomic Physics Q.8P
Find the wavelength of the three longest-wavelength lines of the Paschen series.
Solution:
Chapter 31 Atomic Physics Q.9CQ
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.
Solution:
Chapter 31 Atomic Physics Q.9P
Find (a) the longest wavelength in the Lyman series and (b) the shortest wavelength in the Paschen series.
Solution:
Chapter 31 Atomic Physics Q.10CQ
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
Solution:
Chapter 31 Atomic Physics Q.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) Showthat the ranges of wavelengths of these two series overlap, (b) Is there a similaroverlap between the Balmer series and the Paschen series? Verify your answer.
Solution:
Chapter 31 Atomic Physics Q.11CQ
(a) In the quantummechanical 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.
Solution:
Chapter 31 Atomic Physics Q.11P
CE Predict/Explain (a) If the mass of the electron were magically doubled, would the ionization energy of hydrogenincrease, 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.
Solution:
(a) If the mass of the electron were magically doubled, than ionization energy of hydrogen would have increase.
(b) The ionization energy would increase because the increased mass would mean the electron would orbit closer to the nucleus and require more energy to move to infinity.
Therefore option I is the best explanation
Chapter 31 Atomic Physics Q.12CQ
Would you expect characteristic X-rays to be emitted, by (a) helium atoms or (b) lithium atoms in their ground state? Explain.
Solution:
Characteristic X ray spectrum of a particular element is observed when an electron in the inner shell is removed from the atom, and an electron from the outer shell occupies the vacant place in the inner shell. Therefore, atoms in the ground state cannot emit characteristic X ray spectrum. Even though if an electron from excited state reaches the ground state does not result an X ray spectrum because the binding energy of He and Li atoms is very much less than the energy of the characteristic X ray spectrum.
Therefore, characteristic X ray spectrum cannot be expected from He and Li atoms that are in ground state.
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.13CQ
The elements fluorine, chlorine, and bromine are found to exhibit similar chemical properties. Explain.
Solution:
Chapter 31 Atomic Physics Q.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 tliree atoms in order of increasing energy. Indicate ties where appropriate.
Solution:
Chapter 31 Atomic Physics Q.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?
Solution:
Chapter 31 Atomic Physics Q.15P
Find the ratio v/c for an electron in the first excited state(n = 2) of hydrogen.
Solution:
Chapter 31 Atomic Physics Q.16P
Find the magnitude of the force exerted on an electron in the ground-state orbit of the Bohr model.
Solution:
Chapter 31 Atomic Physics Q.17P
How much energy is required to ionize hydrogen when it is in the n = 4 state?
Solution:
Chapter 31 Atomic Physics Q.18P
Find the energy of the photon required to excite a hydrogen atom from the n = 2 state to the n = 5 state.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Given the hydrogen atom is in the n = 3 state
Chapter 31 Atomic Physics Q.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 resul ts in eV.
Solution:
Chapter 31 Atomic Physics Q.22P
Initially, an electron is in the n = 3 state of hydrogen. If this electron acquires an additional 1.23 eV ofenergy, what is the value of n in the final state of the electron?
Solution:
Chapter 31 Atomic Physics Q.23P
Identify the initiai and final states if an electron in hydrogen emits a photon with a wavelength of 656 mm.
Solution:
Chapter 31 Atomic Physics Q.24P
IP An electron in hydrogen absorbs a photon and jump to a higherorbit, (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 = 5and 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).
Solution:
Chapter 31 Atomic Physics Q.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
Solution:
Chapter 31 Atomic Physics Q.26P
IP Muonitun Muonium is a hydrogen-like atom inwhich the electronis replaced with a muon, a fundamentalparticle 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 Baimer series of hydrogen? Explain, (c) Calculate the longest wavelength of the Balmer series in muonium.
Solution:
Chapter 31 Atomic Physics Q.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 requiredto 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 relevan t energies.
Solution:
Chapter 31 Atomic Physics Q.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+.
Solution:
Chapter 31 Atomic Physics Q.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 groundstate.
Solution:
Chapter 31 Atomic Physics Q.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).
Solution:
Chapter 31 Atomic Physics Q.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).
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.33P
Ahydrogen 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.
Solution:
Chapter 31 Atomic Physics Q.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 2πr/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, λ = 2πr/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.
Solution:
Chapter 31 Atomic Physics Q.35P
Find the de Broglie wavelength of an electron in the ground state of the hydrogen atom.
Solution:
Chapter 31 Atomic Physics Q.36P
Find an expression for the de Broglie wavelength of an electron in the nth state of the hydrogen atom.
Solution:
Chapter 31 Atomic Physics Q.37P
What is the radius of the hydrogen-atom Bohr orbit shown in Figure?
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.39P
What are the allowed values of ℓ when the principal quantum number is n = 5?
Solution:
Chapter 31 Atomic Physics Q.40P
How many different values of mℓ are possible when the principal quantum number is n = 4?
Solution:
Chapter 31 Atomic Physics Q.41P
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.43P
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.46P
CE How many eiectrons can occupy (a) the 2p subshell and (b) the 3p subshell?
Solution:
Chapter 31 Atomic Physics Q.47P
CE (a) How many eiectrons can occupy the 3d subshell? (b) How many electrons can occupy the n = 2shell?
Solution:
Chapter 31 Atomic Physics Q.48P
Solution:
Chapter 31 Atomic Physics Q.49P
Give the electronic configuration for the ground state of carbon.
Solution:
Chapter 31 Atomic Physics Q.50P
List the values of the four quantum numbers (n, ℓ, mℓ, ms)for each of the electrons in the ground state of neon.
Solution:
Chapter 31 Atomic Physics Q.51P
Give the electronic configuration for the ground state of nitrogen.
Solution:
Chapter 31 Atomic Physics Q.52P
Give a list of all possible sets of the four quantum numbers (n, ℓ, mℓ, ms) for electrons in the 3s subshell.
Solution:
Chapter 31 Atomic Physics Q.53P
Give a list of all possible sets of the four quantum numbers (n, ℓ, mℓ, ms) for electrons in the 3p subshell.
Solution:
Chapter 31 Atomic Physics Q.54P
List the values of the four quantum numbers (n, ℓ, mℓ, ms) for each of the electrons in the ground state of magnesium.
Solution:
Chapter 31 Atomic Physics Q.55P
The configuration of the outer electrons in Ni is 3d8 4s2. Write out the complete electronic configuration for Ni.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.57P
Generalize the results of Problem 56 and show that the number of different sets of quantum numbers for the n thshell is 2n2.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.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 liest 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.
Solution:
(a) In an X-ray tube, the wavelength of the characteristic X-rays stays the same if the energy of the electrons striking the target is increased.
(b) 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.
Therefore option III is the best explanation.
Chapter 31 Atomic Physics Q.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.
Solution:
The wave length of the radiation that excites a fluorescent material is less than the wavelength of the radiation the material emits.
Explanation:
In fluorescence, a high – frequency photon raises an electron to an excited state. When electron drops back to the ground state, it may do so by way of various intermediate states. The jumps between intermediate states produce photons of lower frequency, which are observed as phenomenon of fluorescence.
The frequency of the radiation that excites a fluorescent material is greater than the frequency of the radiation the material emits. But frequency is inversely proportional to the wavelength.
The wave length of the radiation that excites a fluorescent material is less than the wave length of the radiation the material emits.
Chapter 31 Atomic Physics Q.61P
Using the Bohr model, estimate the wavelength of the Kα X-ray in nickel (Z = 28).
Solution:
Chapter 31 Atomic Physics Q.62P
Using the Bohr model, estimate the energy of a Kα X-ray emitted by lead (Z = 82).
Solution:
Chapter 31 Atomic Physics Q.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 Kα X-rays emitted by iron?
Solution:
Chapter 31 Atomic Physics Q.64P
An electron drops from the L shell to the EC shell and gives off an X-ray with a wavelength of 0.0205 nm. What is the atomic number of this atom?
Solution:
Chapter 31 Atomic Physics Q.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 Kα 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.
Solution:
Chapter 31 Atomic Physics Q.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 photorefracti ve 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?
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.69GP
The electronic configuration of a particular carbon atom is 1s22s22p13s1. Is this atom in its ground state or in an excited state? Explain.
Solution:
Chapter 31 Atomic Physics Q.70GP
The electronic configuration of a particular potassium atom is 1s22s22p63s23p63d1. Is this atom in its ground state or in an excited state? Explain.
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.72GP
Find the minimum frequency a photon must have it it is to ionize the ground state of the hydrogen atom.
Solution:
Chapter 31 Atomic Physics Q.73GP
Solution:
Chapter 31 Atomic Physics Q.74GPThe electron in a hydrogen atom makes a transitionfrom the n = 4 state to the n = 2 state, as indicated in R (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.
Solution:
Chapter 31 Atomic Physics Q.75GP
IP Referring to Problem, 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 and n = 1 states of hydrogen? Explain.
Problem
74 · · The electron in a hydrogen atom makes a transitionfrom the n = 4 state to the n = 2 state, as indicated in R (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.
Solution:
Chapter 31 Atomic Physics Q.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 μ 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.)
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.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?
Solution:
Chapter 31 Atomic Physics Q.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 correspondingto this wavelength?
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.81GP
Find the approximate wavelength of Kβ 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.)
Solution:
Chapter 31 Atomic Physics Q.82GP
Referring to the hint given in Problem, estimate the wave- ‘ length of La X-rays in molybdenum.
Solution:
Chapter 31 Atomic Physics Q.83GP
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 He+. Spectral lines in the Pickering series have wavelengths given by
In this expression, n = 5,6,7,,… (a) Do you expect the constant C to be greater than, less than, or equal to the Rydberg constant R? Explain. (b) Find the numerical value of C. (c) Pickering lines with n = 6, 8, 10, … correspond to Balmer lines in hydrogen with n = 3, 4, 5, …. Verify this assertion for the n = 6 Pickering line.
Solution:
Chapter 31 Atomic Physics Q.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” inthe 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.
Solution:
Chapter 31 Atomic Physics Q.85GP
Consider a particle of mass m, charge q, and constant speed v moving perpendicular to a uniformmagnetic field of magnitude B, 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: mvr = nh, where n = 1,2,3,…, and h = h/2π.
a. Show that the radii of its allowed orbits have the following values:
Solution:
Chapter 31 Atomic Physics Q.86GP
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
Solution:
Chapter 31 Atomic Physics Q.87GP
Show that the time required for an electron in the nth Bohr orbit of hydrogen to circle the nucleus once is given by
Solution:
Chapter 31 Atomic Physics Q.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
Solution:
Chapter 31 Atomic Physics Q.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
Solution:
Chapter 31 Atomic Physics Q.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
Solution:
Chapter 31 Atomic Physics Q.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
Solution:
Chapter 31 Atomic Physics Q.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.
Solution:
Chapter 31 Atomic Physics Q.93IP
Referring to Example 31–3 (a) Which state has a de Broglie wavelength of 3.99 × 10−9 m? (b) Whatis the Bohr radius of this state?
Solution:
