Acceleration of electron in hydrogen atom

In summary, the conversation discusses the calculation of the electric field and force acting on an electron orbiting a hydrogen proton. The resulting acceleration is found to be extremely high, possibly due to the speed of light. The relevance and accuracy of this example in a textbook is questioned.
  • #1
ocohen
24
0
Hello,
I am currently reading about electromagnetic fields:

In one of the examples in the textbook we calculate the electric field of a hydrogen proton. We then compute the electric force acting on the orbiting electron to be

[itex]8.2 \times 10^{-8} N[/itex]

So I thought I could get the acceleration magnitude from this by dividing by the mass of an electron.

[itex] \frac{ 8.2 \times 10^{-8} N }{9.1 \times 10^{-31} kg} = 9 \times 10 ^{22} \frac{m}{s^2}[/itex]

It seems like this is too fast due to speed of light. I'm assuming that the fact that the electron is orbiting somehow allows for this. Are my calculations correct? Any info would be appreciated.
 
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  • #2
What the [...censored out...] is that textbook? It should be withdrawn immediately.
It really makes no sense to use such terms like "electric force between electron and nucleus" and even less "electron centriprocal acceleration".
Or, maybe, the example had been given to show by reductio at absurdum the inapplicability of mechanistical model of atom?
 
  • #3
ocohen said:
It seems like this is too fast due to speed of light.
Acceleration is not speed. Of course you can use this to calculate the classical, non-relativistic speed. (But this sort of semi-classical model must be ditched for a more complete quantum mechanical treatment anyway.)
 

1. What is the acceleration of an electron in a hydrogen atom?

The acceleration of an electron in a hydrogen atom is determined by the attractive force between the positively charged nucleus and the negatively charged electron. This force is described by Coulomb's law and is inversely proportional to the square of the distance between the electron and the nucleus.

2. How is the acceleration of an electron in a hydrogen atom related to its energy?

The acceleration of an electron in a hydrogen atom is directly related to its energy. As the electron gains or loses energy, its acceleration will change accordingly. This is because the acceleration is determined by the electrostatic force, which is influenced by the electron's position and energy level.

3. Can the acceleration of an electron in a hydrogen atom be negative?

No, the acceleration of an electron in a hydrogen atom cannot be negative. This is because the electron is always attracted to the positively charged nucleus, creating a force in the direction of the nucleus. The direction of the acceleration may change, but it will always be a positive value.

4. How does the acceleration of an electron in a hydrogen atom change with distance from the nucleus?

The acceleration of an electron in a hydrogen atom decreases as the distance from the nucleus increases. This is because the electrostatic force between the electron and nucleus is inversely proportional to the square of the distance between them. As the distance increases, the force decreases, resulting in a decrease in acceleration.

5. Is the acceleration of an electron in a hydrogen atom constant?

No, the acceleration of an electron in a hydrogen atom is not constant. As the electron moves in its orbit around the nucleus, its distance from the nucleus changes, causing the force and acceleration to also change. Additionally, as the electron jumps between energy levels, its acceleration will change accordingly.

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