Compared to a sodium atom in the ground state, a sodium atom in the excited state must have

The first excited state is the same configuration as the ground state, except for the position of one electron.

As an example, sodium goes through a #3s -> 3p# transition.

The ground state electron configuration for sodium is:

#color(blue)(1s^2 2s^2 2p^6 3s^1)#

And the first excited state electron configuration for sodium is:

#color(blue)(1s^2 2s^2 2p^6 3p^1)#

This corresponds to an excitation to a first excited state that is less stable; that then leads to a relaxation back down to the ground state. The relaxation emits yellow light (#"589 nm"#).

I end up going through selection rules (which help you predict whether an electronic transition is allowed or forbidden), term symbols, and predicting transitions. That overall tells you how I know that a #3s -> 3p# transition is a real transition for sodium.

(If you want, you can skip the term symbols contextual section; it's optional.)

You may or may not have learned selection rules yet, but they aren't too difficult to take note of. They would help you determine how to write electron configurations for excited states.

SELECTION RULES

The selection rules govern how an electron is observed to transition (excite upwards or relax downwards) from one orbital to another.

Formally, they are written as:

#color(blue)(DeltaS = 0)#
#color(blue)(DeltaL = 0, pm1)#

#color(blue)(L + S = J)#

#:. color(blue)(DeltaJ = 0, pm1)#

where #DeltaS# is the change in intrinsic angular momentum of the electron (spin multiplicity is #2S + 1#), #DeltaL# is the change in orbital angular momentum, and #DeltaJ# is the change in the total angular momentum.

It is helpful to know the selection rules if you want to predict how an excited state configuration can be written just based on the atom's (correct) ground state configuration.

EXAMPLES OF ELECTRONIC EXCITATION TRANSITIONS

Allowed:

An example of an allowed electronic transition upwards of one unpaired electron to an empty orbital:

#color(green)(2s -> 2p)# (#color(green)(DeltaS = 0#, #color(green)(DeltaL = +1)#, #color(green)(DeltaJ = 0, pm1)#)

#DeltaL = +1# because for #s#, #l = 0#, and for #p#, #l = 1#. Thus, #DeltaL = +1#.

#DeltaS = 0# because the electron didn't get paired with any new electron. It started out unpaired, and it stayed unpaired (#m_s^"new" = m_s^"old"#), so #DeltaS = m_s^"new" - m_s^"old" = 0#.

Forbidden:

An example of a forbidden electronic transition upwards of one unpaired electron to an empty orbital:

#color(green)(3s -> 3d)# (#color(green)(DeltaS = 0)#, #color(green)(DeltaL = color(red)(+2))#, #color(green)(DeltaJ = 0, pm1, color(red)(pm2))#)

#DeltaL = +2# because for #s#, #l = 0#, and for #d#, #l = 2#. Thus, #DeltaL = +2#, which is larger than is allowed, so it is forbidden.

#DeltaS# is still #0# because it's the same electron transitioning as before, just towards a different orbital.

TERM SYMBOLS / CONTEXT

"I've never seen #L#, #S#, or #J# before. Huh? What are they used for?"

You can read more about them here:
http://socratic.org/scratchpad/3616fa1583309e7c0ed2

DISCLAIMER: The above link explains term symbols for context. It helps to know this, but you don't have to know this like the back of your hand unless you are taking Physical Chemistry.

APPLICATION OF THE SELECTION RULES

Alright, so let's apply the selection rules themselves. I gave examples already, so let's work off of the allowed transition example and change it a little bit. The values for #L#, #S#, and #J# are pretty similar.

Let us examine this energy level diagram for sodium:

You can see lines on the diagram going from the #3s# orbital to two #3p# orbital destinations. That indicates either an excitation from the #3s# to the #3p# or a relaxation from the #3p# to the #3s#.

These two lines are marked #589.6# and #589.0#, respectively, in #"nm"#, so what you see happening is that sodium makes its #"589 nm"# excitation transition (upwards), and then relaxes (downwards) to emit yellow light.

Therefore, a common excitation/relaxation transition sodium makes is:

Excitation Transition: #3s -> 3p# (#DeltaS = 0#, #DeltaL = +1#, #DeltaJ = 0, +1#)

Relaxation Transition: #3p -> 3s# (#DeltaS = 0#, #DeltaL = -1#, #DeltaJ = 0, -1#)

(Term symbol notation:

#""^2 S_"1/2" -> ""^2 P_"1/2", ""^2 P_"3/2"#, excitation

#""^2 P_"1/2", ""^2 P_"3/2" -> ""^2 S_"1/2"#, relaxation)

So the ground state electron configuration for sodium is:

#color(blue)(1s^2 2s^2 2p^6 3s^1)#

And the first excited state electron configuration for sodium is:

#color(blue)(1s^2 2s^2 2p^6 3p^1)#

Lastly, an easy way to remember what transitions are allowed is to note that electronic transitions on energy level diagrams are diagonal, and involves adjacent columns.

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Johana Jeon 1A Posts: 30 Joined: Sun Feb 12, 2017 3:00 am

Postby Johana Jeon 1A » Sat Jul 08, 2017 4:34 pm

What does it mean for an electron configuration to represent a ground state or an excited state of an atom?Is it talking about the opposite / same spin?

In 2.39: Determine whether each of the following electron configurations represents the ground state or an excited state of the atom given.

Dabin Kang 1B Posts: 22 Joined: Fri Jun 23, 2017 11:39 am Been upvoted: 1 time

Postby Dabin Kang 1B » Sat Jul 08, 2017 5:24 pm

The ground state electron configuration of an element is the same as the regular configuration in which the electrons are in the lowest possible energy state. For example, the ground state electron configuration of oxygen is 1s2 2s2 2p4.The excited state electron configuration shows when an electron is excited and jumps into a higher orbital. For example, sodium in its excited state would have an electron configuration of 1s2 2s2 2p6 3p1, compared with its ground state of 1s2 2s2 2p6 3s1.

For 2.39, I believe that a, b, and c are excited, while d is in the ground state.

Sarah_Wilen Posts: 62 Joined: Fri Jun 23, 2017 11:39 am Been upvoted: 4 times

Postby Sarah_Wilen » Sat Jul 08, 2017 5:39 pm

The ground state in an atom is when electrons are in the lowest possible energy level. In this state, the electrons have the lowest potential energy. What I mean by low potential energy is that there is nowhere for the electron to "fall". Potential energy is the energy possessed by the electron by virtue to its position relative to others. If I had a piano on a cliff, it will have high potential energy because it has the potential to fall down (potential energy converting to kinetic energy). When the piano has crashed to the ground on a cartoon character, the piano is in its "ground state" because it possesses the lowest potential energy. The piano is in the lowest position relative to its surroundings, so it is in its lowest energy state. Like the piano on the ground, the atom in its ground state means it is in its lowest energy state. All elements on the periodic table are in their ground states.In the question, the only configuration for a ground state atom is d. It follows the rules for electron configuration filling in the ground state...-Aufbau's principle: electrons must fill the lowest energy shells first. (see picture attached)-Hund's rule: when filling sub-levels, electrons must not be spin paired in the orbitals until each orbital contains one electron and no orbital can have two electrons with the same spin.-Pauli Exclusion Principle: no two electrons can have the same quantum numbers. An orbital can only hold 0,1, or 2 electrons. The electrons must have opposite spins if there are 2 electrons in the orbital.On the other hand, above ground states are "excited states". These are states with higher energy than the one of the ground state. If you shoot the atom with a photon, then the photon may be absorbed, so the electrons of the atom will jump from the ground state to an excited state (the difference between the two energies of the final and initial state is the energy of the photon that got absorbed). In an excited state, not all electrons are in the lowest possible energy levels.For example, in the question, a (carbon) is not in the ground state, and it doesn't follow Hund's rule. The electrons in 2p were already spin paired in the orbital before each orbital contained one electron. An easy way to determine if the electron is in the excited state is to compare it to its ground state. If you see electrons have been "moved" to a higher orbital before filling the lower orbital, then that atom is in an excited state. Hope this somewhat helped!

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