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For a hydrogen atom, consider an electron moving in a circular orbit of radius r, with mass m and charge e. What is the total energy of this orbiting electron?
- -e²/2r
- -e²/r
- -me²/r
- -1/2 e²/r
Correct answer: -e²/2r
Solution
The total energy of an electron in a circular orbit around a proton is the sum of its kinetic and potential energy. The kinetic energy is given by (1/2)mv², and the potential energy due to electrostatic attraction is -e²/r. When calculated for a stable orbit, the total energy simplifies to -e²/2r, which accounts for the balance between kinetic and potential energy.
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