Explanation Write the expression for the electrostatic force between the proton and the electron. F e = k e 2 r 2 Here, F e is the electrostatic force, k is the constant, e is the charge of the electron and r is the distance between the masses. Write the expression for the gravitational change in the force. F g = G M e M m r 2 Here, F g is the gravitational force, G is the gravitational constant, M is the mass and r is the radius. To account change in the force replace K e 2 with G M e M m . Write the expression for the radius. r n = n 2 h 2 4 π 2 G M e M m (I) Here, r n is the Bohr radius and n is the Bohr state of the electron. Write the expression for energy. E n = − 2 π 2 G 2 m e 2 m m 2 n 2 h 2 (II) Write the expression Bohr state. n = 4 π 2 G M m 2 M e r n h 2 (III) Conclusion: Substitute 6.626 × 10 − 34 J ⋅ s for h , 1 for n , 6.67 × 10 − 11 N ⋅ m / kg 2 for G , 7.35 × 10 22 kg for m m and 5.98 × 10 24 kg for m e in equation (I) to find r n . r n = ( 6.626 × 10 − 34 Js ) 2 n 2 4 π 2 ( 6.67 × 10 − 11 Nm 2 / kg 2 ) ( 7.35 × 10 22 kg ) 2 ( 5.98 × 10 24 kg ) = n 2 ( 5.16 × 10 − 129 m ) Substitute 6.626 × 10 − 34 J ⋅ s for h , 1 for n , 6.67 × 10 − 11 N ⋅ m / kg 2 for G , 7

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

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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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Chapter 37, Problem 92GP

Chapter 37, Problem 94GP

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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

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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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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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Chapter 37 Solutions