Deriving the electron speed from a specified orbital

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SUMMARY

The discussion centers on calculating the speed of an electron in the n = 3 state of a Hydrogen atom using the equation for energy, En = -E0(z^2/n^2). The user attempts to derive the electron's speed by applying the momentum-energy relationship, p = E/c, and subsequently using p = mv to find velocity. The user expresses confusion regarding the accuracy of their calculations and seeks clarification on whether E = pc is applicable to electrons, particularly given that the total energy of the electron is negative in this state.

PREREQUISITES
  • Understanding of quantum mechanics, specifically the Bohr model of the Hydrogen atom.
  • Familiarity with the concepts of energy and momentum in physics.
  • Knowledge of the relationship between energy, mass, and velocity (E=mc²).
  • Basic grasp of the implications of negative energy states in quantum systems.
NEXT STEPS
  • Study the derivation of electron energy levels in the Hydrogen atom using the Bohr model.
  • Learn about the energy-momentum relation and its implications for particles with mass.
  • Explore the concept of negative energy states in quantum mechanics.
  • Investigate the relationship between velocity, mass, and momentum for subatomic particles.
USEFUL FOR

Students of physics, particularly those studying quantum mechanics, and anyone interested in the behavior of electrons in atomic structures.

jason0294
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[Mentor's note: this thread was moved from a non-homework forum, therefore it does not use the normal template for homework questions]

What is the speed of the electron in terms of the speed of the light when it is in the n = 3 state in the Hydrogen atom?

I started with this equation to find the energy En=-E0(z^2/n^2)
From that i used the momentum=E/c and found momentum then derived v from p=mv
The system keeps saying I am wrong, is there anything specific I am missing or maybe an equation i should be using instead?
 
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jason0294 said:
What is the speed of the electron in terms of the speed of the light when it is in the n = 3 state in the Hydrogen atom?

I started with this equation to find the energy En=-E0(z^2/n^2)
From that i used the momentum=E/c and found momentum then derived v from p=mv

Read http://en.wikipedia.org/wiki/Energy–momentum_relation

Is E=pc true for an electron?

The total energy of the electron in the Hydogen atom is negative. What do you think, why?

ehild
 

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