Electron revolutions in Bohr model

In summary, on the average, an electron in the n = 2 state will make about 5.1516 x 1015 Hz of rotations in 10-8 seconds.
  • #1
Kavorka
95
0

Homework Statement


On the average, a hydrogen atom will exist in an excited state for about 10-8 s before making a transition to a lower energy state. About how many revolutions does an electron in the n = 2 state make in 10^-8 s?

Homework Equations



L = mvr = Iω = nħ
rn = n2a0/Z

The Attempt at a Solution



Finding the angular momentum from ħ and n=2 is just plugging in numbers. Where I'm confused is how to get the number of revolutions from the angular momentum. It would be easy to find if I had ω, but I have no idea how to calculate I in this context. On the other hand, I could find the radius of the orbit from the second equation from a0, n=2 and Z=1. If I had that and the mass of the electron, I could find the electron's velocity. From rn I could also find the circumference of the orbit and calculate the number of revolutions when t = 10-8 s from that. I don't have time to work out the math right now but I will tomorrow and I wanted to post this early. Which approach would be best?
 
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  • #2
Your first approach might be easier. From mechanics, you should have learned the formula for the moment of inertia of a particle moving in a circle.

The second approach will also work. For both approaches you will need to know the mass of the electron, which is easy to find. Also, in both approaches you will need to use the formula for rn.

[Edit: I think both approaches require about the same amount of effort.]
 
  • #3
I looked around and found it. So I = mr2n?
 
  • #4
Yes.
 
  • #5
I'm having an issue.

So rn = a0n2/Z = 2.12 x 10 -10 m

and L = nħ = 2.10914 x 10-34 m2kg/s

ω = L/I = L/mrn2

When I plug this in I get 5.1516 x 1015 Hz, while the back of the book says 8.22 x 1014 Hz
 
  • #6
Make sure you distinguish between angular frequency ##\omega## and frequency ##f##. Angular frequency does not have units of Hz.
 
  • #7
Ah, thank you!
 

Related to Electron revolutions in Bohr model

1. How does the Bohr model explain electron revolutions?

The Bohr model proposes that electrons orbit the nucleus of an atom in specific energy levels or shells, each with a fixed distance from the nucleus. The electrons move in circular orbits and can jump between energy levels by absorbing or emitting energy.

2. Why are there only certain allowed energy levels in the Bohr model?

The allowed energy levels in the Bohr model correspond to the specific energies that an electron can have in its orbit around the nucleus. These levels are determined by the balance between the attractive force of the nucleus and the repulsive force of the electron's momentum.

3. How does the Bohr model explain the stability of atoms?

The Bohr model explains the stability of atoms by proposing that electrons occupy specific energy levels and do not lose energy as they orbit the nucleus. This prevents the electrons from spiraling into the nucleus and maintains the overall stability of the atom.

4. What is the significance of the Bohr model in modern atomic theory?

The Bohr model was a significant advancement in understanding the structure of atoms and laid the foundation for modern atomic theory. It introduced the concept of quantized energy levels and helped explain the stability and behavior of atoms.

5. Are there any limitations to the Bohr model?

Yes, the Bohr model is limited in its ability to fully explain the behavior of atoms. It does not account for the wave-like behavior of electrons or the concept of electron spin. It also cannot fully explain the behavior of multi-electron atoms and molecules.

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