# Electromagnetic field affect on hydrogen atom energy levels

If hydrogen atom is in the ground energy state it must be hitted by photon with energy higher than electron proton energy binding which is 13,6 eV according quantum mechanics. Proton have positive charge and create electric field which hold electron. This electric field at bohr radius has value $$E =\frac{e}{4\pi \epsilon a^2_0} = 514\ \frac{GV}{m}$$ Bohr radius is $$a_0 = 5,29*{10}^{-11}\ m$$

Frequency of photon with 13,6 eV is $$\nu = \frac{E_1}{h} = \frac{13,6\ eV}{6,626 * 10^{-34}\ Js} = 3,284\ PHz$$

Suppose that the anthenna is which radiates electromagnetic wave with 100 MHz frequancy. According to quantum mechanics electromagnetic field is quantized. Each photon has 100 MHz frequancy so the energy of each photon is to small to break electron-proton bond of hydrogen atom in ground state and also smaller than difference between ground and second energy state. I have some questions in this moment. Can electromagnetic wave with electric intensity much higher than electric field generated by proton bonding electron break electron-proton bond even if energy of each photon is lower then difference between ground and next energy state of hydrogen atom? What is difference between situations when electromagnetic field move and passing across hydrogen atom and when stationary electric field generated by charged body passing across hydrogen atom? Do electromagnetic field change energy levels distribution of hydrogen atom when it passing across this atom?

• Commented Dec 26, 2023 at 15:14

In the perturbative limit when the external electric field is much smaller then the internal electric field ($$E_{ext} \ll E_{int}$$), then yes, DC and AC electric fields perturbatively modify the energy levels via the DC and AC Stark shifts.

In the non-perturbative limit, $$E_{ext} \gg E_{int}$$, then yes, the external electric field can ionize the atom. It is true that a single RF photon has nowhere near enough energy to excite an atom, much less ionize it. But, if there is a very strong RF field, we can model it as causing excitation or ionization through a many-photon transition.

The interaction between an electromagnetic field and a hydrogen atom can affect its energy levels through the processes of absorption and emission of photons. The interaction is described by the theory of quantum mechanics. Here are some key points:

1. Absorption of Photons

2. Emission of Photons

3. Shifts in Energy Levels

4. Zeeman Effect

5. Non-Perturbative Effects

It's important to note that these effects are subject to the laws of quantum mechanics and depend on the characteristics of the electromagnetic field, such as its frequency, intensity, and polarization.

In summary, electromagnetic fields can influence the energy levels of a hydrogen atom through absorption and emission of photons, as well as through shifts caused by external electric or magnetic fields. These phenomena are fundamental to the study of atomic and molecular interactions with electromagnetic radiation.