[makbook11]

One of the syllabus statements in my syllabus was: "Each orbital [in an atom] has a defined energy state for a given electronic configuration and chemical environment."

I was confused about what this exactly means -- how does the electronic configuration of an atom change the energy state of an orbital? What does "chemical environment" mean here (I'm guessing it means whether the atom's bonded with other elements) and how does it affect the energy states of orbitals? More generally, what exactly does "energy state" mean? I've been told that electrons fill orbitals with lower energy states first, but does a higher energy state simply mean the electrons in that orbital have more kinetic energy?

Thank you so much for your *delete me*

[Irlanur]

To me, this statement does not make any sense.

[Corribus]

One of the syllabus statements in my syllabus was: "Each orbital [in an atom] has a defined energy state for a given electronic configuration and chemical environment."

There's nothing wrong with this statement from my perspective.

It is common and in fact necessary for spectroscopists to discriminate between orbitals and states. A common approach when trying to determine the allowed energies of electrons in atoms is to define/calculate orbital characteristics by solving for a single electron. For an atom, we call this a "hydrogenic" system, because hydrogen has only one electron, but the approach can work for molecules as well. One-electron orbitals have a characteristic energy and probability density. However with the exception of hydrogen, atoms have more than one electron. What you would do then is fill electrons into the orbitals determined for a one-electron system, but the electrons in a multi-electron system interact with each other. These electron-electron interaction energies can be treated for after the fact using various variational or perturbation methods.

Thus we define a State as a particular arrangement or configuration of electrons, and the State Energy differs from the Orbital Energy because of the specific electron-electron interactions in the given electron configuration.

Example:

In helium you have two electrons. The simplest way to solve this problem is to determine the hydrogenic orbitals for a nuclear core charge of 2, and then fill in both electrons into this orbital. Then you need a way to estimate, because it cannot be determined analytically, how much the true energy differs of this orbital differs from that of a hydrogen orbital by virtue of the fact that the two electrons interact with each other. There are many theoretical methods available to do this.

In the Ground State, which is the lowest energy state, both electrons are in a "1S orbital", where "1S" is a designation for a hydrogen orbital. No, it is not energetically the same as a hydrogen 1S orbital, but it shares many of the same characteristics (shape, say) of a hydrogen 1S orbital, so we usually preserve the nomenclature.  The spins of these electrons are opposite due to the Pauli Exclusion rule.

In an Excited State, one of these electrons is promoted to a higher lying orbital, say the "2S orbital".  Now you have one electron in the 2S orbital and one electron in the 1S orbital - this is your electron configuration. As in the Ground State, this Excited State has a specific associated energy based on the interaction energy between the two electrons, which is different from the interaction energy between the electrons when they are in the Ground State. Morever, because the two electrons are in different orbitals, they no longer need to spin pair. Thus for this configuration you actually have two States - one in which the spins are parallel and one in which they are antiparallel. (Actually, the spin designations are a bit more complicated than this, but in the interest of keeping things simple...) As you might guess, the mutual orientations of the spins also have different energetic interactions. These two States are usually called singlet and triplet states. And then, you actually have coupling between the spin states and the orbital angular momentum of the electrons, which leads to even more possible states.

The important thing is that each of these States has its own unique, quantized energy value, and the number of states depends on what the electron (orbital) configuration is, because this defines what the potential interactions are. It is transitions between these Electron States that are measured by various spectroscopy techniques, and which also give rise to, for example, atomic and astronomical spectral patterns that are characteristic of the elements (i.e., it's how we determine the chemical composition of faraway stars). You might imagine that the number of possible States quickly gets very large, and spectroscopists have developed bookkeeping methods, such as Term Symbols, that can be used to quickly refer to what States are involved in a given spectroscopic transition.

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

The "Chemical Environment" aspect of the statement I think just refers to the fact that the energies of the various (atomic) states are sensitive to other nearby electrostatic systems. If you have two atoms and bring them close enough together, the electrons will begin to interact with each other (and the electrons in one atom will interact with the nucleus of the other). Alternatively, it can mean the solvent your atom/molecule is dissolved in, which can greatly affect the state energies. (Look at the solvent-dependence of fluorescence color, for example.) Another good example that is relevant is the Zeeman Effect, or the associated Stark Effect.

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

If you put some systems in an external magnetic field, previously degenerate States (i.e., states that have the same energy) will split because they interact with the external field differently. In the aforementioned example of helium, I called one of the Excited States a "triplet". It is called a triplet because it actually involves three states that are usually degenerate. These states are distinguished by the direction of the total electron spin. (One in which the spins of the two electrons are both "up", one in which they are both "down" and one in which they are antiparallel.) Normally, it doesn't matter which way the spin vector is going. But it does matter in an external field, where one state becomes slightly higher in energy, and state becomes slightly lower in energy, and the other stays the same.  Triplet = three. Spectroscopically a transition to this state from the Ground State would look like one peak normally, but would look like a triplet when performed in an external magnetic field. This is a good example of how the external environment can impact the energies of atomic or molecular States, even if it's not usually a factor that is important to calculating the properties of an orbital.

[Irlanur]

What you write is all right, but I still don't think that it has a meaning to say that "an orbital has an energy state".

1) what does it mean that an orbital "has" a state? a system is in a state. you can describe that state with a set of orbitals and some kind of combination of these (e.g. a slater determinant). in the hydrogen atom an orbital IS an electronic state.
2) whats an "energy state"?

bottom line: the author of this sentence might be well aware of all the maths and physics behind it, but the sentence is at most just inappropriate language.

[Corribus]

I hear what you're saying (see what you're writing?) but at some point I think parsing semantics reaches a point of diminishing returns, no?

[Irlanur]

If it was a student's sentence I guess it would be ok. But it should be possible for a Professor/teacher to use an exact language. especially if it comes to more or less complicated topics. Usually, inappropriate language is a sign of insufficient understanding.

[Mitch]

For a high school class, I would definitely let that statement slide.

[bestsciencetutor]

One of the syllabus statements in my syllabus was: "Each orbital [in an atom] has a defined energy state for a given electronic configuration and chemical environment."

I was confused about what this exactly means -- how does the electronic configuration of an atom change the energy state of an orbital? What does "chemical environment" mean here (I'm guessing it means whether the atom's bonded with other elements) and how does it affect the energy states of orbitals? More generally, what exactly does "energy state" mean? I've been told that electrons fill orbitals with lower energy states first, but does a higher energy state simply mean the electrons in that orbital have more kinetic energy?

Thank you so much for your *delete me*

So I would say that is question is definitely overly complicated.  Unfortunately it is trying to account for thinks that you may not have learned yet about electron configurations and bonding.  HOWEVER, you are on the right track from what I can see in your answers so far.

The statement is accounting for how the electron configuration and orbitals can change based on bonding to another atom like you guessed.  Also your guess of higher orbitals having more kinetic energy although not technically right tells me you are definitely have a great thinking mind.  Instead of using the word kinetic energy I would call it potential energy because of the distance of the orbital to the nucleus.  Although to me these two terms on interchangeable because it depends on the perspective you are thinking about.

The last part I think you are missing (probably because you were never taught it) is what is called orbital hybridization.  This is when orbitals can change energy states.  This usually happens when atoms bond together.  Electrons take a different orbital path when they are involved in a bond and therefore that different path corresponds to a different energy level.  If you want to learn about orbital hybridization I first suggest you study Lewis Structures (Electron Dot Structures).  This will help you pair pictures on page or in your mind to how the hybrid orbitals work

[Corribus]

There is a lot of incomplete and misleading information in the previous post. As an example, I don't really like using the word "electron" and "path" in the same sentence, because path implies a trajectory, and trajectory implies a defined point in space and vector direction of motion, both of which are completely at odds with modern quantum theory.

[Irlanur]

So I would say that is question is definitely overly complicated.  Unfortunately it is trying to account for thinks that you may not have learned yet about electron configurations and bonding.  HOWEVER, you are on the right track from what I can see in your answers so far.

The statement is accounting for how the electron configuration and orbitals can change based on bonding to another atom like you guessed.  Also your guess of higher orbitals having more kinetic energy although not technically right tells me you are definitely have a great thinking mind.  Instead of using the word kinetic energy I would call it potential energy because of the distance of the orbital to the nucleus.  Although to me these two terms on interchangeable because it depends on the perspective you are thinking about.

The last part I think you are missing (probably because you were never taught it) is what is called orbital hybridization.  This is when orbitals can change energy states.  This usually happens when atoms bond together.  Electrons take a different orbital path when they are involved in a bond and therefore that different path corresponds to a different energy level.  If you want to learn about orbital hybridization I first suggest you study Lewis Structures (Electron Dot Structures).  This will help you pair pictures on page or in your mind to how the hybrid orbitals work.  Here is an educational page from my website about Lewis Structures.  It is not yet complete but it will give you a good start.

I appreciate the fact that you're going back to the original question, but: many things you write are just wrong.

-kinetic and potential energy are (in the usual formalism) very well defined. They appear as separate terms in the Hamiltonian and their expectation values can be calculated. the orbital energy contains kinetic as well as potential energy.
-there is no such thing as an orbital path.
-hybridization is a mathematical, not a physical thing. I know that it's written everywhere that an atom has to "hybridize before bonding". but it's not a physical phenomenon. it's just a different orbital basis set.