# Formula for ionization potential reduction

• Goldhelmeth
In summary, the reduction in ionization potential in a high density plasma, where free electrons are in close proximity to ions, affects the ground energy state of electrons in helium-like atoms. To solve this problem, the Stewart and Pyatt model is commonly used, which utilizes the Debye length. However, more research is needed to determine the new excited state of He1+ in a plasma with an electric field.
Goldhelmeth
Homework Statement
Calculate the ionization potential reduction of He1+ in the framework of the Bohr model and
interpret the results concerning the existence of ground and excited states:
a) in the center of the sun,
b) for the average density of the sun at kTe=1300 eV.
Relevant Equations
*see images
Hello,

Firstly I am not sure of understanding the problem, I believe that this reduction is related to a high density plasma where the free electrons are very close to the ions and so the ions cannot be considered as separate bodies... I also believe it affects the ground energy state of electrons inside hydrogen like atoms (helium +1).
For solving this problem I found that every solutions used the Stewart and Pyatt model. This model uses the debeye lengh. But as you can see it uses an other model... I wished I could provide more to the community to start with but I have been on this problem for hours and I cannot find annything...

Firstly, I think we can solve the ionization potential of He1+ at ground state (1) easily with the Bohr model, as the atom now have 1 nucleus (with 2 protons) and 1 electron, similar to the Hydro atom with a larger nucleus.

In the sun, I understand that ionized gas (He1+) located in an electric field (a gas discharge plasma) is not an equilibrium system, therefore the Helium atoms might now "ground" at the new excited state, and we can calculate the corresponding ionization potential for both a) and b), thus deriving the reduction in ionization potential by subtracting (1). Although I'm not equipped with enough knowledge to determine the new excited state that of He1+ in a) and b), I think you can visit "Excitation of helium atoms in collisions with plasma electrons in an electric field " by Smirnov, B. M. (2013) to research more on the problem.

## 1. What is the formula for ionization potential reduction?

The formula for ionization potential reduction is IP = IP0 - ΔIP, where IP is the ionization potential of the atom, IP0 is the ionization potential of the isolated atom, and ΔIP is the ionization potential reduction due to the presence of other atoms or molecules.

## 2. How is the ionization potential reduction calculated?

The ionization potential reduction is calculated by subtracting the ionization potential of the isolated atom (IP0) from the ionization potential of the atom in a compound (IP), as represented by the formula IP = IP0 - ΔIP.

## 3. What factors affect the ionization potential reduction?

The ionization potential reduction is affected by factors such as the electron affinity of the atom, the electronegativity of the neighboring atoms, and the distance between atoms in the compound.

## 4. Why is the ionization potential reduction important in chemistry?

The ionization potential reduction is important in chemistry because it helps to explain the reactivity and stability of atoms in compounds. It also plays a role in the formation of chemical bonds and the behavior of electrons in molecules.

## 5. Can the ionization potential reduction be negative?

Yes, the ionization potential reduction can be negative. This means that the ionization potential of the atom in a compound is lower than the ionization potential of the isolated atom. This can occur when the neighboring atoms have a high electron affinity and/or electronegativity, making it easier for the atom to lose an electron.

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