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

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SUMMARY

The velocity of an orbiting electron in an atom cannot be defined as a single value due to the principles of quantum mechanics. Instead, the electron's state is described by a wave function, denoted as ψ(x,y,z) for position and ψ(v_x,v_y,v_z) for velocity. The probability of measuring a specific position or velocity is proportional to the square of the wave function's magnitude, |ψ|². In quantum mechanics, electrons do not have definite velocities or positions, contrasting with classical mechanics where such values can be calculated using centripetal force equations.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with wave functions and their representations
  • Knowledge of probability distributions in quantum systems
  • Basic concepts of classical mechanics, particularly centripetal force
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  • Study the implications of wave-particle duality in quantum mechanics
  • Explore the mathematical formulation of wave functions in quantum systems
  • Learn about the Heisenberg Uncertainty Principle and its relation to position and velocity
  • Investigate the concept of stationary states and their significance in quantum mechanics
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Students of physics, quantum mechanics enthusiasts, and researchers interested in atomic behavior and electron dynamics will benefit from this discussion.

Maalolan
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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??
 
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Maalolan said:
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 [itex]\psi(x,y,z)[/itex]. 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 [itex](x,y,z)[/itex] will be proportional to [itex]|\psi(x,y,z)|^2[/itex].

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 [itex]\psi(v_x,v_y,v_z)[/itex]. So, the probability of measuring velocity value [itex](v_x,v_y,v_z)[/itex] is proportional to [itex]|\psi(v_x,v_y,v_z)|^2[/itex]. 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.
 

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