# Where does the radial probability of an electron equation come from?

• brock321
In summary, the conversation discusses the search for a simplified explanation of how the position of an electron can be determined, specifically in relation to the radial wavefunction. The ideal gas equation is used as an example to demonstrate the desired level of simplicity. The conversation also touches on the origin of wavefunctions and the calculation of the radial probability at the Bohr radius.
brock321
Hey

I am looking into how the position of an electron is found. I have seen a derivation for radial wavefunction http://farside.ph.utexas.edu/teaching/qmech/lectures/node79.html but this is too complex. Ideally, I would like a very simplified version of this which leads me to understand how it is possible to know the position of electron (the probability).

For example, in kinetic theory we derive the ideal gas equation by looking at the length of a cube etc... that explanation of how we get the ideal gas equation is very intuitive - can anyone provide a simplified version of the radial distribution function Pn,l(r)=r2Rn,l(r)2
?

or - can anyone just explain what is used inorder for us to know the position of an electron? I know it comes from wavefunctions - but where does wavefunction come from?

thanks

I worked out that the radial probability of finding an electron at the bohr radius was 5 x 10$^{-17}$

Does this sound reasonable? It seems like a very small chance!

## What is the radial probability of an electron equation?

The radial probability of an electron equation is a mathematical expression that describes the likelihood of finding an electron at a certain distance from the nucleus of an atom. It is based on the quantum mechanical model of the atom and takes into account the energy level of the electron and the shape of the orbital it occupies.

## Why is the radial probability of an electron important?

The radial probability of an electron is important because it helps us understand the behavior of electrons in atoms. It allows us to predict the likelihood of finding an electron at a certain distance from the nucleus, which is crucial for understanding chemical bonding and other properties of elements.

## Where does the equation for radial probability of an electron come from?

The equation for radial probability of an electron comes from the Schrödinger equation, which is the fundamental equation of quantum mechanics. It was developed by Erwin Schrödinger in 1926 and describes the behavior of quantum particles, such as electrons, in terms of wave functions.

## What are the variables in the radial probability of an electron equation?

The variables in the radial probability of an electron equation include the principal quantum number (n), which represents the energy level of the electron, and the radial distance (r), which is the distance from the nucleus to the electron. Other variables may also be included depending on the specific form of the equation being used.

## How is the radial probability of an electron equation used in chemistry?

The radial probability of an electron equation is used in chemistry to determine the electron density of an atom, which is important for understanding chemical bonding and reactivity. It also helps explain the properties of different elements, such as their ionization energy and atomic size.

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