The Classical Atomic Model

In summary: Yes, you're right. When I was posting, I was thinking "radial" wasn't the best word here, but I was just being a bit lazy.
  • #1
Shackleford
1,656
2
Calculate the speed and radial acceleration for an electron in the hydrogen atom. Do the same for the Li++ ion.

v = e (4pie0mr)^(-1/2)

ar = (v^2)/r

r ~ 10^-10 m

v = 2.24 x 10^6

The book makes note that we can allow a nonrelativistic treatment since the velocity ~ .007c.

And for the lithium ion I simply multiplied this by the square root of three since the charge would be +3e from the three-proton lithium atom.

However, calculating the radial acceleration yields phenomenally high accelerations: 1.012 x 10^23. Now, I know I'm doing something wrongly here.
 
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  • #2
You're not doing anything wrong. Your sense of "normal" is just off because the speed and radius of the electron's orbit in the Bohr model are not typical values you encounter. Even though the electron is moving at a non-relativistic speed, it's still moving really fast, and the radius of its orbit is very small. Combined, they result in an acceleration that only seems ridiculous because your intuition is based on everyday experiences.
 
  • #3
vela said:
You're not doing anything wrong. Your sense of "normal" is just off because the speed and radius of the electron's orbit in the Bohr model are not typical values you encounter. Even though the electron is moving at a non-relativistic speed, it's still moving really fast, and the radius of its orbit is very small. Combined, they result in an acceleration that only seems ridiculous because your intuition is based on everyday experiences.

Well, I base it on the c speed limit. lol. At that acceleration, even with the theoretical 10^-10 s lifespan the velocity would still far exceed c.
 
  • #4
Radial acceleration only changes the direction an object moves, not its speed.
 
  • #5
Shackleford said:
At that acceleration, even with the theoretical 10^-10 s lifespan the velocity would still far exceed c.

Would it?:wink:

Remember, velocity and acceleration are vectors. They have both a magnitude and a direction. In this case, only the direction of the velocity changes, not its magnitude.
 
  • #6
vela said:
Radial acceleration only changes the direction an object moves, not its speed.

http://bluejaunte.files.wordpress.com/2010/01/double_facepalm.jpg [Broken]

I know that. Crap. Now, I feel silly. Sorry. It only changes the direction of the velocity vector, not its magnitude.
 
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  • #7
vela said:
Radial acceleration only changes the direction an object moves, not its speed.

In this case, yes. But in general, this isn't true of course.
 
  • #8
gabbagabbahey said:
In this case, yes. But in general, this isn't true of course.
Yes, you're right. When I was posting, I was thinking "radial" wasn't the best word here, but I was just being a bit lazy.
 

1. What is the Classical Atomic Model?

The Classical Atomic Model, also known as the Rutherford Model, is a model of the atom proposed by Ernest Rutherford in 1911. It describes the atom as having a dense, positively charged nucleus at its center, surrounded by negatively charged electrons in circular orbits.

2. How is the Classical Atomic Model different from the Bohr Model?

The Bohr Model is an improvement upon the Classical Atomic Model, as it introduced the concept of energy levels and quantized electron orbits. In the Classical Model, electrons were thought to move in circular orbits, while in the Bohr Model, they were described as moving in specific energy levels or shells around the nucleus.

3. What is the significance of the Classical Atomic Model?

The Classical Atomic Model was significant in that it was the first model to propose the existence of a dense, positively charged nucleus at the center of the atom. This model also helped to explain the results of Rutherford's gold foil experiment, which showed that most of the mass of an atom is concentrated in its nucleus.

4. What are the limitations of the Classical Atomic Model?

While the Classical Atomic Model was a major breakthrough in understanding the structure of the atom, it had several limitations. It failed to explain the stability of atoms, as electrons moving in circular orbits would eventually lose energy and spiral into the nucleus. It also did not account for the wave-like behavior of electrons, which is a fundamental aspect of quantum mechanics.

5. How did the Classical Atomic Model lead to the development of modern atomic theory?

The Classical Atomic Model served as a stepping stone towards the development of modern atomic theory. The limitations of this model led to the development of the Bohr Model, which in turn paved the way for the development of quantum mechanics and the understanding of subatomic particles. Today, the Classical Atomic Model is still used as a simplified representation of the atom, but it has been largely replaced by more accurate and complex models.

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