# What causes different energy levels in atoms with multiple electrons?

• Goodver
In summary, the conversation discusses the calculations and equations used to determine the total energy on an energy level for atoms. It is noted that these equations only hold true for a single proton and electron, and that for atoms with more than one electron, additional terms must be included to account for the Coulomb interaction between electrons. A simplified formula for the energy of the valence electron can be derived for alkali atoms.
Goodver
From the calculations of total energy on an energy level we end up with rhe equation which consists of constants only, except of the principal quantum number.

Since equation does not include any unique variables, such as number of protons or electrons in an atom, what makes then different atoms have diferent energy levels?

these calculations for Hydrogen, I assume, the number of electrons somehow determines the energies on the levels, so for different atom with more than 1 electron equations should vary. I also assume that reduced mass caused by different number of protons for different atoms should not cause much of influence.

or energy on a level is a sort of a superposition of waves of all electrons on this level? => sum of energies?

what determines unique energies on levels for different atoms?

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These equations are derived for a nucleus consisting of a single proton, with one electron "orbiting" around it. Very similar equations can be obtained for any charge ##Z## of the nucleus, but again with only one electron. If more than one electron is present, then there are addition terms in the Hamiltonian corresponding to the Coulomb interaction between electrons. This breaks the spherical symmetry and such simple equations can't be derived anymore. Only in the special case of alkali atoms (single valence electron), can an approximate simple formula for the energy of the valence electron be obtained (quantum defect theory).

1 person

## What is Hydrogen?

Hydrogen is the first element on the periodic table and is the lightest and most abundant element in the universe. It has one proton and one electron, making it the simplest element.

## What is Rydberg's Constant?

Rydberg's Constant, also known as the Rydberg constant, is a fundamental physical constant that appears in the equations governing the energy levels of hydrogen atoms. It is named after the Swedish physicist Johannes Rydberg, who first derived the formula for calculating it.

## How is Rydberg's Constant used in science?

Rydberg's Constant is used in various fields of science, including atomic physics, spectroscopy, and quantum mechanics. It is used to calculate the energy levels and wavelengths of spectral lines in hydrogen atoms, as well as other one-electron systems.

## What is the value of Rydberg's Constant?

The value of Rydberg's Constant is approximately 1.0974 × 10^7 per meter (m^-1). This value may vary slightly depending on the units used and the accuracy of the measurement.

## How was Rydberg's Constant discovered?

Rydberg's Constant was first derived by Johannes Rydberg in 1888 based on the spectral lines of hydrogen. He noticed a pattern in the wavelengths of these lines and used mathematical equations to derive the constant. It was later experimentally confirmed by other scientists and has since been used in various fields of science.

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