Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 37, Problem 93GP
To determine
The allowed energies and radii of motion and to check whether the quantization of the energy and radius is apparent or not.
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Suppose that the uncertainty in position of an electron is equal to the radius of the n=1n=1 Bohr orbit, about 0.529×10−10m0.529×10−10m.
A) Calculate the minimum uncertainty in the corresponding momentum component.
Express your answer in kilogram meters per second.
B) Compare this with the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.
Compare this with the magnitude of the momentum of the electron in the Bohr orbit.
a) This is greater than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.
b) This is the same as the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.
c) This is less than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.
As the Earth moves around the Sun, its orbits are quantized. (a) Follow the steps of Bohr’s analysis of the hydrogen atom to show that the allowed radii of the Earth’s orbit are given by where n is an integer quantum number, MS is the mass of the Sun, and ME is the mass of the Earth. (b) Calculate the numerical value of n for the Sun–Earth system. (c) Find the distance between the orbit for quantum number n and the next orbit out from the Sun corresponding to the quantum number n + 1. (d) Discuss the significance of your results from parts (b) and (c).
Physicist's have been able to create hydrogen-like atoms in which the electron has been replaced by a muon, an elementary particle that has the same basic properties as the electron except its mass is 210 times larger and its lifetime is a few microseconds.
a) Assuming that the Bohr model accurately describes such an atom, what is the lowest energy that the muon in this atom can have (in eV)?
b) What is the radius of its effective "orbit" in this state? (Hint: What changes in the formulas we developed for the Bohr model?)
Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 37.2 - Prob. 1AECh. 37.2 - Prob. 1BECh. 37.4 - Prob. 1CECh. 37.7 - Prob. 1DECh. 37.7 - Prob. 1EECh. 37.11 - Prob. 1FECh. 37 - Prob. 1QCh. 37 - Prob. 2QCh. 37 - Prob. 3QCh. 37 - Prob. 4Q
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