Question

The energy of an electron in the ground state of a hydrogen atom is $ - 13.6eV$. Find the kinetic energy and potential energy of an electron in this state.

Answer 1

Hint: The energy given I the question is the total energy of the electron in the ground state. The total energy is the sum of kinetic energy and the potential energy of an electron in that state.

Complete step-by-step answer:
Total energy of the electron in the ground state of hydrogen atom is given,
$E = - 13.6eV$
Here, a general question arises why the energy of the electron is negative?
The answer to this question is that the negative sign simply indicates that, to take the electron from its "orbit" around the nucleus and move it to infinity where the potential energy between the electron and the nucleus is zero requires us to supply at least $ + E$. If we supply more than $ + E$ the electron will have some kinetic energy left when it reaches infinity
We know that,
The kinetic energy of the electron,
$KE = - E$
$KE = - ( - 13.6)eV$
$KE = 13.6eV$
We know that the total energy of the electron is the sum of kinetic energy and the potential energy of an electron in that state.
So,
$E = KE + PE$
$ - 13.6 = 13.6 + PE$
$PE = - 27.2eV$

Additional information:
Some of the limitations of Bohr’s atomic theory is-
(a) The theory could not explain the atomic spectra of the atoms containing more than one electron or multielectron atoms.
(b) Bohr’s theory failed to explain the fine structure of the spectral lines.
(c) Bohr’s theory could not offer any satisfactory explanation of the Zeeman effect and the Stark effect.
(d) It was not in accordance with Heisenberg’s uncertainty principle.

Note:
For the sake of the question, we assume that the electron is rotating around the nucleus at a fixed distance from the nuclei. This approach is only correct for solving for single-electron species but for multi-electron species, this approach gives inconsistent results. We cannot find the absolute distance of the electron from the nucleus because according to Heisenberg’s uncertainty principle the momentum and position of a microscopic particle cannot be determined to absolute accuracy.