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

[nophun6]

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!

 

[Andrew Mason]

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

 

[kyle8921]

The energy needed for an electron in the lowest orbital to be freed from its proton, or ionize the atom, is indeed -13.6 eV. This energy is the minimum amount required for the electron to overcome the attractive force of the proton and move away from it.

In terms of the second question, the concept of energy needed for an object to escape the gravitational force of another object is similar to the energy needed for an electron to escape the proton in the Bohr model. In both cases, there is a central force (gravity or electrostatic force) that holds the objects together, and in order for one object to break free from the other, it must have enough energy to overcome this force. In the Bohr model, the energy is provided by an external source (such as an electric field), while in the case of planets, it is provided by the object's own kinetic energy.