Physical Science (12th Edition), Standalone Book
12th Edition
ISBN: 9781260150544
Author: Bill W. Tillery
Publisher: McGraw Hill Education
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Chapter 8, Problem 5PEB
To determine
Energy required to remove one electron from
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with n= 4. the energy that must be absorbed by the atom is
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3. Consider a monatomic linear with equilibrium separation a. Suppose the outer
electrons (of mass m) in a given atom move with a displacement different from that
of the corresponding ion core (of mass M). Let the displacement of the ion core s be:
Us = uei(Ksa-wt)
and the displacement of the center of mass of the outer electrons associated with ion s
be:
V = vei(Ksa-wt)
Each ion core is assumed to interact only with its own outer electrons with a force
proportional to the displacement of the electron distribution from the nucleus, and the
force constant is C₂. However, neighboring electron distributions interact with a force
constant C₁.
a) Show that
-w² Mus = C₂ (vs - Us)
-w²mvs = C₂ (us - Vs) + C₁ (Vs+1 + Vs-1-2vs)
b) Substitute for the displacements, and solve the resulting simultaneous equations.
Find an expression for w².
c) Take the limit as m → 0 (the mass of electrons is much smaller than that of the ion
core), and show that the dispersion relation for the acoustic mode is…
Chapter 8 Solutions
Physical Science (12th Edition), Standalone Book
Ch. 8 - Prob. 1ACCh. 8 - Prob. 2ACCh. 8 - Prob. 3ACCh. 8 - 4. Millikan measured the charge on oil droplets...Ch. 8 - Prob. 5ACCh. 8 - Prob. 6ACCh. 8 - Prob. 7ACCh. 8 - Prob. 8ACCh. 8 - Prob. 9ACCh. 8 - Prob. 10AC
Ch. 8 - Prob. 11ACCh. 8 - Prob. 12ACCh. 8 - Prob. 13ACCh. 8 - Prob. 14ACCh. 8 - Prob. 15ACCh. 8 - Prob. 16ACCh. 8 - Prob. 17ACCh. 8 - Prob. 18ACCh. 8 - Prob. 19ACCh. 8 - Prob. 20ACCh. 8 - Prob. 21ACCh. 8 - Prob. 22ACCh. 8 - Prob. 23ACCh. 8 - Prob. 24ACCh. 8 - Prob. 25ACCh. 8 - Prob. 26ACCh. 8 - 27. Elements that have properties of both the...Ch. 8 - Prob. 28ACCh. 8 - Prob. 29ACCh. 8 - Prob. 30ACCh. 8 - Prob. 31ACCh. 8 - Prob. 32ACCh. 8 - Prob. 33ACCh. 8 - Prob. 34ACCh. 8 - Prob. 35ACCh. 8 - Prob. 36ACCh. 8 - Prob. 37ACCh. 8 - Prob. 38ACCh. 8 - Prob. 39ACCh. 8 - Prob. 40ACCh. 8 - Prob. 41ACCh. 8 - Prob. 42ACCh. 8 - Prob. 43ACCh. 8 - Prob. 44ACCh. 8 - Prob. 45ACCh. 8 - Prob. 46ACCh. 8 - Prob. 47ACCh. 8 - Prob. 48ACCh. 8 - Prob. 49ACCh. 8 - Prob. 1QFTCh. 8 - Prob. 2QFTCh. 8 - Prob. 3QFTCh. 8 - Prob. 4QFTCh. 8 - Prob. 5QFTCh. 8 - Prob. 6QFTCh. 8 - Prob. 7QFTCh. 8 - Prob. 8QFTCh. 8 - Prob. 9QFTCh. 8 - Prob. 10QFTCh. 8 - Prob. 11QFTCh. 8 - Prob. 12QFTCh. 8 - Prob. 1FFACh. 8 - Prob. 2FFACh. 8 - Prob. 3FFACh. 8 - Prob. 4FFACh. 8 - Prob. 5FFACh. 8 - Prob. 6FFACh. 8 - Prob. 1PEACh. 8 - Prob. 2PEACh. 8 - Prob. 3PEACh. 8 - Prob. 4PEACh. 8 - Prob. 5PEACh. 8 - Prob. 6PEACh. 8 - Prob. 7PEACh. 8 - Prob. 8PEACh. 8 - Prob. 9PEACh. 8 - Prob. 10PEACh. 8 - Prob. 11PEACh. 8 - Prob. 12PEACh. 8 - Prob. 13PEACh. 8 - Prob. 14PEACh. 8 - Prob. 15PEACh. 8 - Prob. 16PEACh. 8 - Prob. 17PEACh. 8 - Prob. 18PEACh. 8 - Prob. 19PEACh. 8 - Prob. 1PEBCh. 8 - Prob. 2PEBCh. 8 - Prob. 3PEBCh. 8 - Prob. 4PEBCh. 8 - Prob. 5PEBCh. 8 - 6. If the charge-to-mass ratio of a proton is 9.58...Ch. 8 - Prob. 7PEBCh. 8 - 8. Using any reference you wish, write the...Ch. 8 - Prob. 9PEBCh. 8 - 10. Referring to Figure 8.16 only, write the...Ch. 8 - 11. An electric motor draws a current of 11.5 A in...Ch. 8 - Prob. 12PEBCh. 8 - Prob. 13PEBCh. 8 - Prob. 14PEBCh. 8 - Prob. 15PEBCh. 8 - Prob. 16PEBCh. 8 - Prob. 17PEBCh. 8 - Prob. 18PEBCh. 8 - Prob. 19PEB
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- An electron is in the hydrogen atom with n = 5. (a) Find the possible values of L and Lz for this electron, in units of h. (b) For each value of L, find all the possible angles between L → and the z-axis. (c) What are the maximum and minimum values of the magnitude of the angle between L →and the z-axis?arrow_forwardThe allowed energies of a simple atom are 0.0 eV, 4.0 eV, and 6.0 eV. An electron traveling at a speed of 1.5x106 m/s collisionally excites the atom. Part A) What is the minimum speed the electron could have after the collision? Part B) What is the maximum speed the electron could have after the collision?arrow_forwardCan nuclei of the same element have different values of Z? Of N? Of A? Can nuclei of different elements have the same values of Z? Of N? Of A?arrow_forward
- Recall for an the hydrogenic (single electron) atom 2s (r) = 2,0,0 (r, 0, 4) Φ2p (r) = Φ2,1,0 (r,θ, φ) - = 2p (7) = 2p_ (F) = 2,1,1 (r, 0, 6): = 2,1,-1 (r, 0,6) 1 4√2π/² p 1 3/2 ao 4√/2πа = 2 δεν παρ Tº 3/2 ao 8√πа 3/2 ao 1) e-r/2² ao e ○ (02s (71)2p, (72) + O2p. (71)02s (72)) O 02s (1) 2po (2) ○(28 (71)2p, (72) – $2p. (71)¢2s (72)) O 02s (1)02s (F2) T -T 12a0 •/200 cos 0, /2ao sin 0 etic. r/2ao sin 0 e-iç Consider the helium atom (two electron system). Suppose the spin part is one of the triplet. Which of the following can be a possible space part?arrow_forwardThe energy of a hydrogen atom is 12.09 eV above its groundstate energy. As a multiple of h, what is the largest angular momentum that this atom could have?arrow_forwardAn atom has completely filled inner shells and a single valence electron in an excited p state. The filled inner shells have an orbital momentum equal to zero. A magnetic field is applied. What is the set of possible angles between the magnetic field and the orbital angular momentum? O 45°, 135° 90° O 45° O 45°, 90°, 135° O 45°, 90°arrow_forward
- what energy is required to remove the electron from a hydrogen atom in the n= 11 state? Let the constant hcR= 13.6 eVarrow_forwardAccording to the modern atomic theory, how many electrons are found in n = 2?arrow_forward(a) The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N2+ ion? (b) Estimate the energy of the least strongly bound level in the L shell of N2+. (c) The doubly charged ion P2+ is formed by removing two electrons from a phosphorus atom. What is the ground-state electron configuration for the P2+ ion? (d) Estimate the energy of the least strongly bound level in the M shell of P2+arrow_forward
- The electron in a certain hydrogen atom has an angular momentum of 2.583×10−34 J.s. What is the largest possible magnitude for the z-component of the angular momentum of this electron? For accuracy, use h=6.626×10−34 J⋅s. find Number Unitsarrow_forwardA sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective (b) r = (c) r= Number i Number i Number i Units Units Unitsarrow_forwardA sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective = Number i 2.04 (b) _r= (c)_r= Number i 5.29E-11 Number i 2.12E-11 Units No units Units m Units m ♥arrow_forward
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