[Licensed Criminal]

Hello, new guy here!

I'm in need of some clarification, because my chemistry book is sometimes too vague. I've been under the impression that electrons in an orbital are able to have a range of energy, and that they cannot move into higher sub-shells unless a precise amount of energy (corresponding to the difference between the orbital the electron is currently occupying and the next highest one) is provided. Is this an accurate statement? The electrons having a 'range' of energy in an orbital is the part I'm unsure about.

Oh yes, and why is it that in elements up to Nickel, the 3d sub-shell has a higher energy than the 4s sub-shell?

[xiankai]

electrons in an orbital are able to have a range of energy

the potential energy of an electron increases as it moves away from the nucleus. since an orbital is probability cloud where an electron is most likely to be found, it does not represent a fixed area. hence electrons in an orbital are able to have a range of energy.

precise amount of energy (corresponding to the difference between the orbital the electron is currently occupying and the next highest one)

as they are referring to the difference in energy of energy levels, it is only a rough guideline.

why is it that in elements up to Nickel, the 3d sub-shell has a higher energy than the 4s sub-shell?

due to overlapping of subshells, the 3d subshell has a higher energy level. the 4s subshell is a sphere shape while that of the 3d is of four balloons extending from the nucleus in four directions. since the 3d subshell happens to be extended further than the 4s subshell, it has a higher energy level (generally).

[Dan]

I've been under the impression that electrons in an orbital are able to have a range of energy, and that they cannot move into higher sub-shells unless a precise amount of energy (corresponding to the difference between the orbital the electron is currently occupying and the next highest one) is provided.

No, I don't think that's accurate. Quantum theory predicts that electrons may only possess certain allowed energies (ie. energy levels rather than a continuum). This is a demonstration of quantisation, and is the reason that orbitals have specific energies. Each allowed energy has an electron density function associated with it, it is this density function which is the orbital. Thats how I see it.

Oh yes, and why is it that in elements up to Nickel, the 3d sub-shell has a higher energy than the 4s sub-shell?

This is true for the transition metals up to Ni. But not for other previous elements (eg K, Ca).
One argument is that as the effective nuclear charge increases accross the period, the orbitals drop in energy. Since the 4s are more penetrating than the 3d, as we move from K to Ni, the energy of the 4s drops faster than the 3p. The crossover point being Sc I think. This effect is even more pronounced by ionisation (as this inreases effective nuclear charge even more).

[Ψ×Ψ]

Dan's right.  Energy is quantized. 

[FeLiXe]

If an orbital is populated only for a short time its energy is not precise because of the incertainty principle. maybe that was meant

[english]

I disagree.

According to my general chem text, starting with the transition series the 3d electrons become lower in energy than the 4s electrons.

The increasing nuclear charge as we progress across Period 4 once we hit Scandium causes the filling d orbitals to drop in energy, and reside closer to the nucleus. 

Thus, a switch in energies occur between the s and d orbitals.  When iron ionizes, for example, it loses its 4s electrons first, then proceeding 3d electrons.



Strange phenomenon but this is as it is explained in my text.

[Mitch]

The 3d electrons are always lower in energy than the 4s electrons period. Your book is wrong.

The energy of configuration might be lower for the 4s to be populated before the 3d, but the energy of the 4s orbital is higher than the 3d.

The energy of configuration takes into account: The energy of the orbital + the exchange energy + electron repulsive force within the same orbital

We've had this exact discussion on the forum many times now.

[english]

The 3d electrons are always lower in energy than the 4s electrons period. Your book is wrong.

The energy of configuration might be lower for the 4s to be populated before the 3d, but the energy of the 4s orbital is higher than the 3d.

The energy of configuration takes into account: The energy of the orbital + the exchange energy + something I can't recall at the moment but we've had this exact discussion on the forum many times now.

You mean the topic starter's book is wrong.   

I referenced my text too.  You don't mean me right?

[Mitch]

of course.

[Dan]

Sorry, my mistake everyone, I meant 3d drops faster than 4s. I was typing in a rush and muddled it (I even threw in a 3p to confuse everyone further). Ignore the second part of my previous post.

[FeLiXe]

the problem is that orbitals are nothing physically real. It's just that the real configuration wavefunction can be approximated by orbitals.

When talking about orbital energies you'd have to specify how you obtain them. Typically you would take Hartree-Fock energies. Hartree-Fock energies do include exchange energies and electron-electron interactions. So the Hartree-Fock energy of the 3d like orbital would be higher than the 4s like one.

[Ψ×Ψ]

When talking about orbital energies you'd have to specify how you obtain them. Typically you would take Hartree-Fock energies. Hartree-Fock energies do include exchange energies and electron-electron interactions.

Waaaait.  You mean electron-electron repulsion, right?  Correlation energy is still neglected, isn't it?

[FeLiXe]

yes, I should have said it includes some electron-electron interaction. but the energy is overestimated because you consider the electrons statistically independent. you have to subtract the correlation energy.

[Ψ×Ψ]

Alright.  I didn't think you would overlook that, it just sounded...off.

[FeLiXe]

to be precise there are three types of correlation:
1. Fermi correlation (because of the Pauli principle)
2. coulomb correlation
3. symmetrical correlation

with a Hartree-Fock method (that uses a Slater determinant) you include the Fermi correlation (as far as I understand it)
the Fermi correlation energy may be the same as the exchange energy, because exchange energy comes from the Slater determinant

for coulomb correlation you need configuration interaction (CI) methods

I don't know what symmetrical correlation is