Are All Triplet States Symmetric in Spin Wavefunction Across Different Atoms?

[Amith2006]

Homework Statement

# The triplet state in helium atom is represented by a symmetric spin wavefunction. Are all triplet states of an atom represented by a symmetric spin wavefunction or is this just in the case of helium atom?

# Fermions are represented by an anti-symmetric total wavefunction. So if a pair of electrons is in the triplet state, it will be represented by a symmetric spin wavefunction and an anti-symmetric space wavefunction because,

Total wavefunction= $$\psi$$(space) x $$\psi$$(spin)

it is said that an anti-symmetric spatial wavefunction implies a greater distance between the electrons when compared to a symmetric spatial wave function as in the case of singlet state. Could anyone please help me in understanding the whole idea behind this?

Homework Equations

The Attempt at a Solution

 

[javierR]

It is said that an anti-symmetric spatial wavefunction implies a greater distance between the electrons when compared to a symmetric spatial wave function as in the case of singlet state. Could anyone please help me in understanding the whole idea behind this?

Try plotting the spatial wavefunctions in the two cases, or find somewhere where they are already plotted.
The anti-symmetric spatial wavefunction means that there is a exp[r1-r2] appearing in the wavefunction instead of exp[-(r1+r2)] for electron 1 and 2. The wavefunction will then have minimal probability amplitude when r1 --> r2 so the electrons' expectation values are furthest from each other.