College Physics (10th Edition)
10th Edition
ISBN: 9780321902788
Author: Hugh D. Young, Philip W. Adams, Raymond Joseph Chastain
Publisher: PEARSON
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Chapter 29, Problem 16P
To determine
What is the maximum orbital
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An 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.”
a) An electron in a hydrogen atom has energy E= -3.40 eV, where the zero of energy is at the
ionization threshold. In the Bohr model, what is the angular momentum of the electron? Express your
result as a multiple of ħ.
Ans.
b) What is the deBroglie wavelength of the electron when it is in this state? Ans.
c) When the electron is in this state, what is the ratio of the circumference of the orbit of the electron
to the deBroglie wavelength of the electron?
Ans.
d) The electron makes a transition from the state with energy E= -3.40 eV to the ground state, that
has energy -13.6 eV. What is the wavelength of the photon emitted during this transition?
Ans.
The average value (or expected value) of r^k, where r is the distance of an electron in the state with principal quantum number n and orbital quantum number leo proton in the hydrogen atom is given by the integral below, where Pnl(r) is a radial probability density of the state with quantum number n, lek is an arbitrary power. For an electron in the ground state of the hydrogen atom.
a) calculate <r>nl in terms of the Bohr radius aB
b) calculate <l/r>nl in terms of aB
c) calculate <U(r)>nl, where U(r) = -e^2/(4piE0r). Respond in eV units.
d) Considering also that the electron is in the ground state, estimate the expected value for two kinetic energy <K> and its mean quadratic velocity v.
e) Is it justifiable to disregard relativistic corrections for this system? Justify.
Chapter 29 Solutions
College Physics (10th Edition)
Ch. 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. 10CQ
Ch. 29 - Prob. 1MCPCh. 29 - Prob. 2MCPCh. 29 - Prob. 3MCPCh. 29 - Prob. 4MCPCh. 29 - Prob. 5MCPCh. 29 - Prob. 6MCPCh. 29 - Prob. 7MCPCh. 29 - Prob. 8MCPCh. 29 - Prob. 9MCPCh. 29 - Prob. 10MCPCh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5PCh. 29 - What is the ratio of the number of different 3d...Ch. 29 - Prob. 7PCh. 29 - Prob. 8PCh. 29 - Prob. 9PCh. 29 - Prob. 10PCh. 29 - For bromine (Z = 35), make a list of the number of...Ch. 29 - (a) Write out the electron configuration (1s2 2s2,...Ch. 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. 27GPCh. 29 - Prob. 28GPCh. 29 - An electron has spin angular momentum and orbital...Ch. 29 - Prob. 30GPCh. 29 - Prob. 31GPCh. 29 - Prob. 32GPCh. 29 - Prob. 33GPCh. 29 - Prob. 34GPCh. 29 - Prob. 35GPCh. 29 - Prob. 36GPCh. 29 - Prob. 37GPCh. 29 - Prob. 38GPCh. 29 - Prob. 39PPCh. 29 - Prob. 40PPCh. 29 - Prob. 41PPCh. 29 - Prob. 42PP
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