Potential and Kinetic Energy of Electron in an Orbit

Potential Energy of Electron
- The potential energy of an electron in an orbit of a hydrogen atom is given by the formula:
Potential Energy = -13.6/n^2 eV, where n is the principal quantum number of the orbit.
- If the potential energy of the electron is -x eV, then we can determine the value of n using the formula: -13.6/n^2 = -x.
- Solving for n, we get n = sqrt(13.6/x).

Kinetic Energy of Electron
- The total energy of the electron in the orbit is the sum of its potential and kinetic energies, given by the formula:
Total Energy = Potential Energy + Kinetic Energy.
- Since the total energy of the electron is constant, we can find the kinetic energy by subtracting the potential energy from the total energy.
Kinetic Energy = Total Energy - Potential Energy.
- Substituting the values, we get:
Kinetic Energy = -13.6/n^2 - (-x) = -13.6/n^2 + x.
- Using the value of n calculated earlier, we can now determine the kinetic energy of the electron in the same orbital.
In conclusion, the kinetic energy of the electron in the same orbital with a potential energy of -x eV can be calculated using the above steps. This demonstrates the relationship between the potential and kinetic energies of an electron in an orbit of a hydrogen atom.

X/2