Explanation Write the expression to obtain the relationship between electric force and the gravitational force. Z e 2 4 π ε 0 = G m e m p Here, e is the charge on the electron, ε 0 is the permittivity in free space, Z is the number of positive charges, G is the gravitational constant, m e is the mass of the electron and m p is the mass of the proton. Write the expression to obtain the radius of the first Bohr orbit. r 1 = h 2 ε 0 π m e Z e 2 Here, r 1 is the radius of the first Bohr orbit, h is the Planck’s constant, ε 0 is the permittivity in free space, m e is the mass of the electron, Z is the number of positive charges and e is the charge on the electron. Re-write the above equation. r 1 = h 2 4 π 2 m e 4 π ε 0 Z e 2 Substitute G m e m p for Z e 2 4 π ε 0 in the above equation. r 1 = h 2 4 π 2 m e 1 G m e m p = h 2 4 π 2 G m e 2 m p (I) Write the expression to obtain the energy of the first Bohr orbit. E 1 = − Z 2 e 4 m e 8 ε 0 2 h 2 Here, E 1 is the energy of the first Bohr orbit, Z is the number of positive charges, e is the charge of the electron, m e is the mass of the electron, ε 0 is the permittivity in free space and h is the Planck’s constant. Re-write the above equation. E 1 = − ( Z e 2 4 π ε 0 ) 2 2 π 2 m e h 2 Substitute G m e m p for Z e 2 4 π ε 0 in the above equation. E 1 = − ( G m e m p ) 2 2 π 2 m e h 2 = − 2 π 2 G 2 m e 3 m p 2 h 2 (II) Conclusion: Substitute 6.626 × 10 − 34 J ⋅ s for h , 6.67 × 10 − 11 N ⋅ m 2 / kg 2 for G , 9.11 × 10 − 31 kg for m e and 1.67 × 10 − 27 kg for m p in equation (I) to calculate r 1 . r 1 = ( 6

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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The Bohr model

Students often get confused between Rutherford’s model and Bohr model of an atom. They interpret the postulates of both these models to be the same, which is incorrect. Rutherford’s model differs from Bohr’s model in the following ways:

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Chapter 37, Problem 70P

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The radius and energy of the first Bohr orbit.

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Chapter 37, Problem 69P

Chapter 37, Problem 71P

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Chapter 37 Solutions

Physics for Scientists and Engineers with Modern Physics

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The radius and energy of the first Bohr orbit.

Solution Summary: The author explains how to obtain the relationship between electric force and gravitational force.

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The radius and energy of the first Bohr orbit.

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Chapter 37 Solutions