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Formula Rydberg Formula for Hydrogen Atom Frequency    Principal quantum number    Rydberg frequency

Formula
Formula: Rydberg Formula for Hydrogen Atom
Hydrogen atom - term diagram (energy levels)

Frequency

Unit
Frequency of electromagnetic radiation in vacuum with which the H atom is irradiated. Frequency is related to the energy of the radiation as follows: \( W ~=~ h \, f \).

Principal quantum number

Unit
This is an integer indicating an energy level of the H atom. The electron in the H atom can occupy an energy state, which is described by \(n\).

It is true: \( n ~\lt~ m \), that is, the \(n\)th energy state is lower than the \(m\)th energy state. The electron in the H atom can be excited to the \(m\)th energy state.

Upper principal quantum number

Unit
This is an integer indicating an energy level of the H atom. The electron in the H atom can occupy this energy state, which is described by \(m\), by being excited into this energy state by a photon. After a short time, the electron falls back to the lower state \(n\) and the H atom emits a photon in the process. The energy of this photon corresponds to the difference of the energy between \(m\) and \(n\) states.

Rydberg frequency

Unit
Rydberg frequency for the hydrogen atom is$$ R_{\text f} ~=~ c \, R ~=~ 3.289 \, 841 \, 95 \,\cdot\, 10^{15} \, \mathrm{Hz} $$ where \(c\) is the speed of light and \( R \) is the Rydberg constant for the H atom: \( R = 1.097 373 15 \,\cdot\, 10^7 \, \frac{1}{\mathrm m} \).

Multiplying the Rydberg frequency by Planck's constant \(h\) yields the energy required to remove the electron from the H atom (i.e., to ionize the H atom):$$ R_{\text f} \, h ~=~ 2.17 \cdot 10^{-18} \, \mathrm{J} ~=~ 13.6 \, \mathrm{eV} $$