What is the velocity of an orbiting electron in an atom?

[Maalolan]

What is the velocity of an orbiting electron in an atom? it wuld be great if anyone can explain it. Shld we calculate from the centrepetal force equation. then it wuld be classical. Any quantum mechanical explanation??

 

[meopemuk]

What is the velocity of an orbiting electron in an atom? it wuld be great if anyone can explain it. Shld we calculate from the centrepetal force equation. then it wuld be classical. Any quantum mechanical explanation??

You probably know that electron in atom does not have a definite position. Electron's state is described by a wave function in the position representation \psi(x,y,z). If you prepare many identical copies of the atom and measure electron's position in each copy, you'll not get the same result each time. Any value of position can be measured, and the probability of measuring position (x,y,z) will be proportional to |\psi(x,y,z)|^2.

The situation is exactly the same with velocities. The state of the electron in atom can be described also by a wavefunction in the velocity representation \psi(v_x,v_y,v_z). So, the probability of measuring velocity value (v_x,v_y,v_z) is proportional to |\psi(v_x,v_y,v_z)|^2. So, there is no definite value of velocity for the electron in atom.


There are special states (plane waves) in which measurements of velocity give certain results, but they are not among stationary states of the electron in atom.

Eugene.