# A Why Energy of 4s is higher than 3d?

1. May 12, 2016

### ImShiva

According to Aufbau principle energy of 3d should be greater than 4s but here 4s is having higher energy. Please anyone explain this.

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2. May 12, 2016

### BvU

Hi ImShiva,

The principle you mention isn't about energy; it's about the order in which orbits are filled.

3. May 12, 2016

### ImShiva

But isn't lower energy implying that orbital must be filled first?

4. May 12, 2016

### BvU

Apparently not !

5. May 12, 2016

### ImShiva

How...? Please explain

6. May 12, 2016

### Khashishi

Lower energy states do indeed fill up before higher energy states. But, the Aufbau principle refers to how additional electrons fill up. An additional electron placed into the 3d state will have higher energy than an electron that is excited into the 3d state with the states below empty. That's because there is repulsion between the electrons. For helium, which has two electrons, there isn't too much interaction between an electron in 3d and in the 1s position, so, the energy isn't that high. Consider hydrogen, which has only one electron. Then the 3d state has the same energy as the 3p and 3s states. When you fill up the lower states, then the 3d state energy rises because it has more interaction with the inner electrons than the 3s and 3p states.

7. May 12, 2016

### ImShiva

So I guess (n+l) energy rule won't work here. What's the rule for energy of states then ?

8. May 12, 2016

### blue_leaf77

The (n+l) rule is for the individual energy of electrons in a subshell denoted by the quantum number $nl$ to form a ground state of the atom, The energy $E_{nl}$ governed by that rule is the energy of each subshell in the ground state of an atom and not the total energy of the atom. In your diagram, it is the total energy of the atom (He atom) which is shown, in particular it shows energy levels including its ground state and the excited states of the form $1s\, nl$ where one electron stays in $1s$ subshell and the other in $nl$ subshell. Again, the (n+l) rule is irrelevant here because the diagram is not about the energy of each subshell in a He atom.
The only rule I know regarding the energy diagram of a $1s\, nl$ He atom is that the energy for orthohelium is always lower than for parahelium for the same $nl$.

9. May 13, 2016

### DrDu

In Helium, the only orbital filled is 1s, so the aufbau principle is correct. The other orbitals are virtual orbitals and not filled, so they are irrelevant for the aufbau principle.

10. May 13, 2016

### Khashishi

For atoms with more than one electron, you need to go into lengthy calculations to come up with energy levels. There are various approximations, to varying degrees of accuracy (e.g. Hartree-Fock). But nothing so simple as the hydrogen atom.

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