My name is Alexander Fufa

**eV**and here I will explain the following topic:# Rydberg Formula: Understanding the Energy Spectrum of the Hydrogen Atom

## Formula

## What do the formula symbols mean?

## Binding energy

`$$ W $$`Unit

`$$ \mathrm{J} = \mathrm{Nm} = \frac{ \mathrm{kg} \, \mathrm{m^2} }{ \mathrm{s}^2 } $$`

Energy required to knock an electron, which is in the \( n \)-th state, out of the hydrogen atom. For example, the binding energy of the electron in the ground state is \( n = 1 \): \( 13.6 \, \mathrm{eV} \).

## Quantum number

`$$ n $$`Unit

`$$ - $$`

Principal quantum number is an integer indicating an energy level of the H atom. The electron in the H atom can occupy this energy state, which is characterized by \(n\).

Here is:

- \( n = 1 \) is the ground state.
- \( n = 2 \) is the first excited state.
- \( n = 3 \) is the second excited state.
- and so on...

**Explanation**

## Video

The Rydberg formula describes the wavelengths \( \lambda\) of lines in the spectrum of the hydrogen atom. However, it also describes the discrete energy levels \( W\) of the hydrogen atom:

Formula anchor
$$ \begin{align} W ~=~ \frac{ 13.6 \, \mathrm{eV} }{ n^2 } \end{align} $$

Formula anchor
$$ \begin{align} \lambda ~=~ \frac{1}{R \, \left( \frac{1}{n^2} - \frac{1}{m^2} \right)} \end{align} $$

Formula anchor
$$ \begin{align} f ~=~ R_{\text f} \, \left( \frac{1}{n^2} ~-~ \frac{1}{m^2} \right) \end{align} $$