- #1

fluidistic

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## Homework Statement

Using Hund's rule, find the fundamental term of an atom whose last incomplete subshell contains 3 electrons d. Do the same with 4 electrons p.

## Homework Equations

The 3 Hund's rules.

## The Attempt at a Solution

By fundamental term I'm guessing they mean the ground state term.

Despite knowing Hund's rules, I don't know how I can start the problem without having the term symbols of the atom(s).

I somehow made an attempt, for the 3 electrons d.

Since the subshell is d, it means each electrons will have the quantum numbers [itex]l=2[/itex]. So that [itex]L=6[/itex]. Also, since there are 3 electrons, [itex]S=3/2[/itex]. Thus J goes from [itex]L-S=9/2[/itex] to [itex]L+S=15/2[/itex].

That d shell is half filled so that J will equal to [itex]9/2[/itex] for the ground state.

L could in principle for 6 (but in practice no?!), this would make my answer as [itex]^{16}H_{9/2}[/itex]. Which is -I'm 100% sure-, totally wrong.

What I don't understand is that L seems to go from 0 to 6 as if one adds the [itex]m_l[/itex] 's of the 3 electrons instead of the [itex]3 l[/itex]'s.

Any help is appreciated.