How Does the Bohr Model Explain Ionization Energy in Hydrogen Atoms?

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The Bohr model of the hydrogen atom calculates that the minimum energy required to ionize an electron in its ground state (n=1) is 13.6 eV. This energy represents the work needed to overcome the attractive force between the electron and proton. The discussion also draws a parallel between this atomic ionization and the gravitational escape energy required for a planet to break free from another planet's gravitational pull. Both scenarios involve adding energy to overcome attractive forces, though the energy levels in atomic systems are more discrete compared to planetary orbits. Understanding these concepts highlights the similarities between atomic and gravitational interactions.
nophun6
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Q: From the Bohr model of the Hydrogen atom, calculate the minimum amount of energy (in eV) an electron in the lowest orbital would need to free it from its proton (i.e., to ionize the atom).

A: would I use the equation: En = - 13.6 / (n^2) ?
If so, an an electron in its ground state would be n= 1
So the answer would be -13.6 eV ?

Q2: If you consider the Bohr model of the atom, where the proton and electron act as two bodies of mass, and the electron escapes from the pull of the proton with the energy found in part A, how is this similar to the energy needed for one body of mass, like a planet, to escape the gravitational force of another planet?

A2: I understand that in order for a planet to escape the gravitational force of another planet energy must be exerted, just as with the proton and electron, but I don't understand what they want for an answer.

Thanks in advance for the help!
 
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nophun6 said:
Q: From the Bohr model of the Hydrogen atom, calculate the minimum amount of energy (in eV) an electron in the lowest orbital would need to free it from its proton (i.e., to ionize the atom).

A: would I use the equation: En = - 13.6 / (n^2) ?
If so, an an electron in its ground state would be n= 1
So the answer would be -13.6 eV ?

Q2: If you consider the Bohr model of the atom, where the proton and electron act as two bodies of mass, and the electron escapes from the pull of the proton with the energy found in part A, how is this similar to the energy needed for one body of mass, like a planet, to escape the gravitational force of another planet?

A2: I understand that in order for a planet to escape the gravitational force of another planet energy must be exerted, just as with the proton and electron, but I don't understand what they want for an answer.
Q1 What is the energy at n = \infty? What is the energy at n =1 ? What is the difference?

Q2 What is the gravitational potential energy of the planet in orbit and what is its escape energy (ie. energy needed to make r = \infty)? It is a similar concept to the Bohr model of the atom except that the energy levels permited for a planet in orbit are much finer than those for an electron obiting a proton. In both cases, as the forces are attractive, energy must be added to remove the obiting body.

AM
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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