How Does the Bohr Model Explain Energy Levels in One-Electron Atoms?

In summary: You may substitute in the value of N and Z for your result. In summary, the allowed Bohr radii are: r = 2.22×10^-12 meters.Your answer for (b) looks correct. You may substitute in the value of k for your result. In summary, the allowed kinetic energy is: k = 4.184×10^-27 Joules.Your answer for (c) looks correct. You may substitute in the value of Uel for your result. In summary, the allowed electric potential energy is: Uel = -8.8×10^-27 Joules.Your answer
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Homework Statement



The Bohr model
The Bohr model correctly predicts the main energy levels not only for atomic hydrogen but also for other "one-electron" atoms where all but one of the atomic electrons has been moved, as as in He+ (one electron removed) or Li++ (two electrons removed). To help you derive an equation for the N energy levels for a system consisting of a nucleus containing Z protons and just one electron answer the following questions. Your answer may use some or all of the following variables: N, Z, hbar, pi, epsilon0, e and m

(a) What are the allowed Bohr radii?
r = Click here to preview your answer.wrong check mark
Click here for help with symbolic formatting.

(b) What is the allowed kinetic energy? Instead of substituting in your answer for part (a) you may use the variable r.
k = Click here to preview your answer.
Click here for help with symbolic formatting.

(c) What is the allowed electric potential energy? Instead of substituting in your answer for part (a) you may use the variable r.
Uel = Click here to preview your answer.
Click here for help with symbolic formatting.

(d) Combining your answers from part (a), (b) and (c) what are the allowed energy levels? our answer should not contain the the variable r (use your result from part (a)).
E = Click here to preview your answer.
Click here for help with symbolic formatting.




(e) The negative muon (μ-) behaves like a heavy electron, with the same charge as the electron but with a mass 207 times as large as the electron mass. As a moving μ- comes to rest in matter, it tends to knock electrons out of atoms and settle down onto a nucleus to form a "one-muon" atom. Calculate the radius of the smallest Bohr orbit for a μ- bound to a nucleus containing 77 protons and 194 neutrons. Your answer should be numeric and in terms of meters.
r = m



The Attempt at a Solution



Tried all solutions for the first one but no luck !
 
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  • #2
First answer is :

(N^2(hbar^2/((1/(4piepsilon0))e^2m)))/Z
 
  • #3
Welcome to PF.

As per forum rules, you must demonstrate an attempt at solving the problem before receiving help.

Your answer for (a) looks correct.
 

FAQ: How Does the Bohr Model Explain Energy Levels in One-Electron Atoms?

What is the Bohr Model?

The Bohr Model, also known as the Bohr atomic model, is a simplified representation of the structure of an atom. It was proposed by Danish physicist Niels Bohr in 1913 and is based on the idea that electrons orbit the nucleus in specific energy levels.

What is the significance of the Bohr Model?

The Bohr Model is significant because it was the first successful attempt to explain the structure of atoms. It also laid the foundation for further developments in quantum mechanics.

How does the Bohr Model differ from the current model of the atom?

The Bohr Model is a simplified representation of the atom, whereas the current model, known as the quantum mechanical model, takes into account the wave-like behavior of electrons and their uncertain positions. The Bohr Model also has a fixed orbit for electrons, while the current model allows for electron movement in a range of energy levels.

What are the limitations of the Bohr Model?

The Bohr Model has several limitations, such as not being able to explain the spectral lines of atoms with more than one electron and not taking into account the wave-like behavior of electrons. It also does not account for the repulsion between electrons, which can affect their energy levels.

What is the importance of the Bohr Model in understanding atomic structure?

The Bohr Model was a crucial step in understanding atomic structure and the behavior of electrons. It helped scientists to visualize the structure of atoms and laid the foundation for further advancements in quantum mechanics. It also led to the development of new technologies, such as the atomic bomb and nuclear power plants.

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