Acceleration of electron in hydrogen atom

[ocohen]

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

8.2 \times 10^{-8} N

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

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

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.

 

[xts]

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 It should be withdrawn immediately.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?

 

[Doc Al]

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.)