Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 29, Problem 27P
To determine
The element it its outermost electron state in a
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A certain element has its outermost electron in a 3p subshell. It has valence +3 because it has three more electrons than a certain noble gas. What element is it?
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…
3.
eV.
Consider an atom of triply ionized beryllium Be³+ with an energy of -9.704
(a) List all the possible states, excluding spin, of the hydrogen atom with this energy.
(b) What is the degree of degeneracy?
(c) What is the maximum possible angular momentum L (as a multiple of ħ)?
Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 29.2 - Prob. 29.1QQCh. 29.2 - Prob. 29.2QQCh. 29.4 - Prob. 29.3QQCh. 29.5 - Prob. 29.4QQCh. 29.6 - Prob. 29.5QQCh. 29.6 - Prob. 29.6QQCh. 29 - Prob. 1OQCh. 29 - Prob. 2OQCh. 29 - Prob. 3OQCh. 29 - Prob. 4OQ
Ch. 29 - Prob. 5OQCh. 29 - Prob. 6OQCh. 29 - Prob. 7OQCh. 29 - Prob. 8OQCh. 29 - Prob. 9OQCh. 29 - Prob. 10OQCh. 29 - Prob. 1CQCh. 29 - Prob. 2CQCh. 29 - Prob. 3CQCh. 29 - Prob. 4CQCh. 29 - Prob. 5CQCh. 29 - Prob. 6CQCh. 29 - Prob. 7CQCh. 29 - Prob. 8CQCh. 29 - Prob. 9CQCh. 29 - Prob. 10CQCh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5PCh. 29 - Prob. 6PCh. 29 - Prob. 7PCh. 29 - Prob. 8PCh. 29 - Prob. 10PCh. 29 - Prob. 11PCh. 29 - Prob. 12PCh. 29 - Prob. 13PCh. 29 - Prob. 14PCh. 29 - Prob. 15PCh. 29 - Prob. 16PCh. 29 - Prob. 17PCh. 29 - Prob. 18PCh. 29 - Prob. 19PCh. 29 - Prob. 20PCh. 29 - Prob. 21PCh. 29 - Prob. 22PCh. 29 - Prob. 23PCh. 29 - Prob. 24PCh. 29 - Prob. 25PCh. 29 - Prob. 26PCh. 29 - Prob. 27PCh. 29 - Prob. 28PCh. 29 - Prob. 29PCh. 29 - Prob. 30PCh. 29 - Prob. 31PCh. 29 - Prob. 32PCh. 29 - Prob. 33PCh. 29 - Prob. 34PCh. 29 - Prob. 35PCh. 29 - Prob. 36PCh. 29 - Prob. 37PCh. 29 - Prob. 38PCh. 29 - Prob. 39PCh. 29 - Prob. 40PCh. 29 - Prob. 41PCh. 29 - Prob. 42PCh. 29 - Prob. 43PCh. 29 - Prob. 44PCh. 29 - Prob. 45PCh. 29 - Prob. 46PCh. 29 - Prob. 47PCh. 29 - Prob. 48PCh. 29 - Prob. 49PCh. 29 - Prob. 50PCh. 29 - Prob. 51PCh. 29 - Prob. 52PCh. 29 - Prob. 53PCh. 29 - Prob. 54PCh. 29 - Prob. 55PCh. 29 - Prob. 57PCh. 29 - Prob. 58PCh. 29 - Prob. 59PCh. 29 - Prob. 60PCh. 29 - Prob. 61PCh. 29 - Prob. 63PCh. 29 - Prob. 64PCh. 29 - Prob. 65PCh. 29 - Prob. 66P
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- What is the maximum number of orbital angular momentum electron states in the n = 2 shell of a hydrogen atom? (Ignore election spin.)arrow_forwardIf an atom has an election in the n = 5 state with m = 3, what are the possible values of l?arrow_forward(a) How many electrons can be in the n=4 shell? (b) What are its subshells, and how many electrons can be in each?arrow_forward
- 1. A hydrogen atom is in p state in M shell. (a) If this hydrogen atom absorbs a photon, it gets excited to the d state in N shell. Draw the energy level diagram of the initial and final hydrogen state and find the wavelength of the photon absorbed. (b) Find the angular momentum of hydrogen in the final state and write down its quantum numbers. (c) After magnetic field of 2 T is applied, hydrogen assumes the lowest energy level. What are the magnetic quantum number in this state and z-component of the angular momentum? (d) Find the value of energy shift in hydrogen state due to magnetic field effect. (e) How much energy (in electron volts) does it take to ionize hydrogen in d state in N shell, while the magnetic field is turned on.arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.arrow_forwardIn the equation below, the Balmer series involves the emission lines (wavelengths) obtained when electrons go from higher energy (excited) level to 1 1 R n' 1 where, R = 1.097 x 107 m-1 %3D -- A. The ground level (n = 1) B. The first atomic level (n = 2) C. The third atomic level (n = 3) D. The fourth atomic level (n = 4) E. The fifth atomic level (n = 4) %3D %3Darrow_forward
- O 36 Sulfur (S) has an atomic number of 16. What is its electron configuration? O 1s 2s 2p°3s-3p O 1s°25-2p°3s°3p O 1s252p 3s²3d* O 1s°252p°3s²3p²arrow_forward2.1. A neutral atom has the following electronic configuration: 1s? 2s² 2p° 3s² 3p³ (a). How many electrons are in the M shell? (b). How many protons are in the atomic nucleus? (c). To which group of the periodic table does this element belong?arrow_forward8. An electron in H atom occupies the state (√eve + R21 a) What is the energy of the electron? b) If you measure the total angular momentum squared (L²), what value(s) you will get and with what probability? c) If you measure the z-component of orbital angular momentum (L₂), what value(s) you might get and with what probability?arrow_forward
- c. n= 2, 1 = 0. 2. Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 3, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.arrow_forwardAn alkali metal atom is in the ground state. The orbital angular momentum equals zero and the spin angular momentum is entirely due to the single valence electron. A magnetic field is applied that splits the ground state energy level into two levels, 65 μeV apart.A photon, absorbed by the atom, induces a transition between the two levels. What is the wavelength of the photon? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, Bohr magneton = μB = 9.27 × 10-24 J/T, 1 eV = 1.60 × 10-19 J) Group of answer choices 19 mm 41 mm 38 mm 25 mm 31 mmarrow_forwardA lithium atom has three electrons, and the 2S1/2 groundstate electron configuration is 1s22s. The 1s22p excited state is split into two closely spaced levels, 2P3/2 and 2P1/2, by the spin-orbit interaction.A photon with wavelength 67.09608 mm is emitted in the 2P3/2 S 2S1/2 transition, and a photon with wavelength 67.09761 mm is emitted in the 2P1/2 S 2S1/2 transition. Calculate the effective magnetic field seen by the electron in the 1s22p state of the lithium atom.arrow_forward
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