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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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.)
The Bohr model correctly predicts the main energy levels not only for atomic hydrogen but also for other "one-electron" atoms where all but one of the atomic electrons has been removed, such as in He+ (one electron removed) or Li++ (two electrons removed).
The negative muon (μ−)behaves like a heavy electron, with the same charge as the electron but with a mass 207 times as large as the electron mass. As a moving μ− comes to rest in matter, it tends to knock electrons out of atoms and settle down onto a nucleus to form a "one-muon" atom. For a system consisting of a nucleus of iridium (Ir192 with 77 protons and 115 neutrons) and just one negative muon, predict the energy in eV of a photon emitted in a transition from the first excited state to the ground state. The high-energy photons emitted by transitions between energy levels in such "muonic atoms" are easily observed in experiments with muons.
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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_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_forward
- Assuming 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_forwardIn 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_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_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_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
- How many revolutions does the electron in the hydrogen atom in the ground state make per second? (h = 6.63x10 Js, mass of clectron = 9.11x101 kg, Bohr radius = 0.053 nm.) A- 6.55x1015 B- 3.28x1015 C- 3.28x10 D- 1.64x105 E- 9.11x105 The ionisation energy of the hydrogen atom is 13.6 eV. If hydrogen atoms in the ground state absorb quanta of encrgy 12.75 eV, how many discrete spectral lines will be emitted as per Bohr's theory? A- 1 В-2 С-4 D- 6 E- zero The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true? A- Its kinetic energy increases and its potential and total energies decrease. B- Its kinetic energy decreases, potential energy increases and its total energy remains the same. C- ts kinetic and total energies decrease and its potential energy increases. D- Its kinetic, potential and total energies decrease. An electron in a Haydrogen atom undergoes a transition from the state n = 4 to n = 2. The energy…arrow_forwardThe electron of a hydrogen atom is in an orbit with radius of 8.46 Å (1 Å = 10-10 m), according to the Bohr model. Which of the following statements is correct? a) The total energy of the orbit is –13.6 eV, and the kinetic energy is +13.6 eV. b) The total energy of the orbit is –0.85 eV, and the potential energy is –1.70 eV. c) The total energy of the orbit is –0.85 eV, and the potential energy is +1.70 eV. d) The total energy of the orbit is –0.85 eV, and the potential energy is –0.85 eV. e) The total energy of the orbit is –3.40 eV, and the potential energy is –6.80 eV.arrow_forwardConsidering the Bohr’s model, given that an electron is initially located at the ground state (n=1n=1) and it absorbs energy to jump to a particular energy level (n=nxn=nx). If the difference of the radius between the new energy level and the ground state is rnx−r1=5.247×10−9rnx−r1=5.247×10−9, determine nxnx and calculate how much energy is absorbed by the electron to jump to n=nxn=nx from n=1n=1. A. nx=9nx=9; absorbed energy is 13.4321 eV B. nx=10nx=10; absorbed energy is 13.464 eV C. nx=8nx=8; absorbed energy is 13.3875 eV D. nx=20nx=20; absorbed energy is 13.566 eV E. nx=6nx=6; absorbed energy is 13.22 eV F. nx=2nx=2; absorbed energy is 10.2 eV G. nx=12nx=12; absorbed energy is 13.506 eV H. nx=7nx=7; absorbed energy is 13.322 eVarrow_forward
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