Energy of electron in hydrogen atom per Bohr

In the Bohr’s model of the Hydrogen atom, the electron is viewed as moving along a circular orbit around the nucleus (which was further generalized onto elliptical orbits by Sommerfeld). In the circular case, the energy of the atom can be expressed directly as a function of the electron’s orbit radius.

Notation:

1. \(e\) (e) is elementary_charge.

2. \(\varepsilon_0\) (epsilon_0) is vacuum_permittivity.

Links:

1. Formula 13.8 on p. 71 of “General Course of Physics” (Obschiy kurs fiziki), vol. 5, part 1 by Sivukhin D.V. (1979).

energy

energy of the Hydrogen atom.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

radius

radius of the electron’s orbit.

Symbol:

r

Latex:

\(r\)

Dimension:

length

law

E = e^2 / (8 * pi * epsilon_0 * r)

Latex:

\[E = \frac{e^{2}}{8 \pi \varepsilon_0 r}\]