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.

 

[denian]

The velocity of an orbiting electron in an atom can be calculated using the classical equation for centripetal force, as you mentioned. This approach assumes that the electron follows a circular path around the nucleus and experiences a centripetal force due to the electrostatic attraction between the electron and the positively charged nucleus.

However, in the quantum mechanical model of the atom, the behavior of electrons is described by wave functions rather than classical trajectories. Therefore, the concept of a specific velocity for an orbiting electron becomes more complex. Instead, we use the concept of momentum, which is related to the wavelength of the electron's wave function.

In quantum mechanics, the momentum of an electron in an atom is described by the Heisenberg uncertainty principle, which states that the more precisely we know the position of an electron, the less we know about its momentum and vice versa. This means that we cannot know the exact velocity of an electron in an atom, but we can calculate its average momentum.

In summary, the velocity of an orbiting electron in an atom cannot be precisely determined, but its average momentum can be calculated using quantum mechanical principles. It is important to note that the behavior of electrons in atoms is complex and cannot be fully explained using classical physics.