What is meant by the orbital approximation for the wave function of a many electron atom?...

What is meant by the orbital approximation for the wave function of a many electron atom? Describe the limitations of this approximation.

Expert Solution

Multi-Electron Atom
The electron of interest feels the individual electric fields of the other electrons and the nucleus.

queen_honey_blossom answered 3 years ago

11) The wave function of a many-electron closed-shell atom can be expressed as a Slater determinant....

11) The wave function of a many-electron closed-shell atom can be expressed as a Slater determinant. A useful property of determinants is that interchanging any two rows or columns changes their sign and therefore that if any two rows or columns are identical, then the determinant vanishes. Use this property to show that (a) no two electrons can occupy the same orbital with the same spin.

The electron configuration of an atom tells us how many electrons are in each orbital. For...

The electron configuration of an atom tells us how many electrons are in each orbital. For example, helium has two electrons in the 1s orbital. Therefore the electron configuration of He is 1s2 part a: What is the ground-state electron configuration of a neutral atom of nickel? Express your answer in condensed form, in order of increasing orbital energy. For example, [He]2s22p2 would be entered as [He]2s^22p^2 . part b: What is the ground-state electron configuration of the oxide ion...

If an electron in an atom has an orbital angular momentum with ml = 4, what...

If an electron in an atom has an orbital angular momentum with ml = 4, what are the components (a) Lorb,z and (b) μorb,z? If the atom is in an external magnetic field that has magnitude 44 mT and is directed along the z axis, what are (c) the potential energy Uorb associated with the electron's orbital magnetic dipole moment and (d) the magnitude of the potential energy Uspin associated with the electron's spin magnetic dipole moment? If, instead, the...

Consider a hydrogen atom with its electron in the nth orbital.

Consider a hydrogen atom with its electron in the nth orbital. Electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm).

What is the number of angular nodes in the wave function for a hypothetical h orbital?...

What is the number of angular nodes in the wave function for a hypothetical h orbital? What would be the lowest valid combination of principal quantum number and angular momentum quantum number that would be valid for an h orbital?

Write the electron configurations and orbital spin diagrams for the neutral atom and the kon of...

Write the electron configurations and orbital spin diagrams for the neutral atom and the kon of the element having the atomic number 12. Based on this information explain the valence number of electrons in the elements responsible for the ion's charge.

If an electron in an atom has orbital angular momentum with ml values limited by

a) If the electron in a hydrogen atom jumps from the 4s orbital to a 2p orbital, will it emit light or will it absorb light?

a) If the electron in a hydrogen atom jumps from the 4s orbital to a 2p orbital, will it emit light or will it absorb light?b) What wavelength will it emit or absorb?

If an electron in an atom has orbital angular momentum with ml values limited by ±2,...

If an electron in an atom has orbital angular momentum with ml values limited by ±2, how many values of (a) Lorb,z and (b) μorb,z can the electron have? In terms of h, m, and e, what is the greatest allowed magnitude for (c) Lorb,z and (d) μorb,z? (e) What is the greatest allowed magnitude for the z component of the electron's net angular momentum (orbital plus spin)? (f) How many values (signs included) are allowed for the z component...

For the Li atom, one electron occupies a 2s orbital, even though the average position of...

For the Li atom, one electron occupies a 2s orbital, even though the average position of an electron in a 2s orbital is further from the nucleus than for an electron in a 2p orbital. Why is this the case?

Question