Hi

I was reading that in a many electron atom (eg. Helium), it is assumed that each electron occupies its own orbital..

thus,the overall wavefunction (w) is w(1).w(2)...

how is this possible?? isn't the 1s orbital of helium filled with 2 electrons so what do they mean that each electron occupy its own orbital?

http://en.wikipedia.org/wiki/Atomic_Orbital

the term orbital refers to the set of quantum numbers which are in fact related to the solution to the wave equations.

Hi! I can help explain the concept of each electron occupying its own orbital in a many-electron atom like Helium.

In a many-electron atom, electrons are distributed in different energy levels and orbitals. These orbitals represent the regions of space where electrons are most likely to be found. Each orbital can hold a specific number of electrons, based on their quantum numbers.

For example, in the case of Helium, the ground state electronic configuration is 1s^2. This means that both electrons are in the 1s orbital, but they each have different quantum numbers. One electron has spin up (↑) and the other has spin down (↓).

So, even though both electrons are in the same orbital, they have different spin states, which are represented by the ↑ and ↓ symbols. This distinction allows us to say that each electron occupies its "own" orbital, taking into account the different spin orientations.

The overall wavefunction of a many-electron atom is a mathematical function that describes the behavior of all the electrons in the system. It is represented as the product of each individual electron's wavefunction, w(1).w(2)..., where w(1) refers to the wavefunction of the first electron and w(2) refers to the wavefunction of the second electron.

So in the case of Helium, the overall wavefunction would be described as w(1, spin up).w(2, spin down), where w(1, spin up) represents the wavefunction of the first electron with spin up and w(2, spin down) represents the wavefunction of the second electron with spin down.

I hope this helps clarify the concept! Let me know if you have any further questions.