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 65P
To determine
The kinetic energy of the Auger electron.
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A 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
Units
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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- For an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the kinetic energy; (c) the potential energy; and (d) the total energy.arrow_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_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 (b)_r= (c)_r= Number i Number i Units Units Unitsarrow_forward
- An electron in chromium moves from the n = 2 state to the n = 1 state without emitting a photon. Instead, the excess energy is transferred to an outer electron (one in the n = 4 state), which is then ejected by the atom. In this Auger (pronounced “ohjay”) process, the ejected electron is referred to as an Auger electron. (a) Find the change in energy associated with the transition from n = 2 into the vacant n = 1 state using Bohr theory. Assume only one electron in the K shell is shielding part of the nuclear charge. (b) Find the energy needed to ionize an n = 4 electron, assuming 22 electrons shield the nucleus. (c) Find the kinetic energy of the ejected (Auger) electron. (All answers should be in electron volts.)arrow_forwardThe Bohr model for the hydrogen atom can be extended to cover other atoms when they are stripped free of all but one electron. When this occurs, the energy levels for the single electron in an atom with atomic number, Z, are given by En = ((-13.6 eV)Z²)/(n²) (see Example 42.4). Calculate the electron energy for the first five energy levels (n = 1 to n = 5) of ionized chlorine (Ci16+). E1 = ev E2 = ev E3 = ev E4 = ev Es = evarrow_forwardAssuming that only a single electron is present and a Bohr model, calculate the mean radius, orbital velocity, and energy of a N=1 electron of hydrogen N=4 electron for lead N=1 electron for plutonium N=1 electron for an element with Z = 142arrow_forward
- In the ground state of the hydrogen atom, the electron has a total energy of -13.6 eV.What are (a) its kinetic energy and (b) its potential energy if the electron is one Bohr radius from the central nucleus?arrow_forwardAn electron is in the nth Bohr orbit of the hydrogen atom. (a) Show that the period of the electron is T = n3t0 and determine the numerical value of t0. (b) On average, an electron remains in the n = 2 orbit for approximately 10 ms before it jumps down to the n = 1 (ground-state) orbit. How many revolutions does the electron make in the excited state? (c) Define the period of one revolution as an electron year, analogous to an Earth year being the period of the Earth’s motion around the Sun. Explain whether we should think of the electron in the n = 2 orbit as “living for a long time.”arrow_forwardIn a hydrogen atom, the small magnetic moment of the proton interacts with the magnetic moment of the electron. This results in a 5.87 meV energy difference between the ms = + 12 and ms = -12 states. What wavelength photon is emitted in a transition between these two states?arrow_forward
- In the ground state of the Hydrogen atom the energy of the electron is E0 = -13.61 eV. What is the energy of the electron in the ground state of the He+ ion? Hints:The He+ ion is a Hydrogen-like structure, it has only one electron.How does the energy of the electron depend on the charge of the nucleus? Is this a bound state? Make sure, your answer has the correct sign. Incorrect. Tries 1/20 Previous Tries What is the energy of the electron in the ground state of the Li++ ion? Tries 0/20 The electron in the He+ ion is excited to the n = 2 principal state. What is the energy of the electron now? Tries 0/20 What is the energy of the electron in the Li++ ion in the n = 2 principal state? Tries 0/20 What is the energy of the electron in the Li++ ion in the n = 3 principal state? Tries 0/20 Take element Z = 83 from the periodic table. Ionize it 82 times so that there is only one electron left orbiting around the nucleus. What is the…arrow_forwardwhat energy is required to remove the electron from a hydrogen atom in the n= 11 state? Let the constant hcR= 13.6 eVarrow_forward
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