# What is Ground-state and Excited state of an atom?Thanks..

Feb 22, 2016

It is essentially the difference between an atom with extra energy (excited-state) and the same atom in its most stable state, with no extra energy (ground-state).

Let's say we looked at sodium ($Z = 11$) as an example. Its electron configuration is:

$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{1}$

If we shine a light source onto sodium that successfully excites the $3 s$ electron into the $3 p$ orbital (a higher-energy orbital), then we've put sodium into its first excited state. We provided some energy that allows the electron to jump into a higher-energy, suitable orbital.

The new configuration is:

$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {p}^{1}$

Of course, we should recognize that the $3 s$ orbital is now empty (we excited it out of that orbital into a higher-energy orbital).

HOW TO PREDICT EXCITED STATES?

By what's known as the "selection rules", we can predict possible excitation pathways.

1. An electron can only jump up into an orbital that retains the total electron spin ($\Delta S = 0$)
2. We must make sure the total change in angular momentum $l$ is exactly $\pm 1$ ($\Delta L = \pm 1$).

Thus, for $\Delta S = 0$, an unpaired electron cannot jump into an orbital with another unpaired electron (or else $\Delta S = \pm 1$, which is not equal to $0$), and you have to go $s \to p$ or $p \to d$ or $d \to f$, but you cannot go $s \to d$ or $p \to f$ in one step (because $\Delta L \ne \pm 1$).

For instance:

• $3 s \to 3 p$ is allowed. $l$ changed by exactly $\pm 1$.
• $3 s \to 5 p$ is allowed, if you have enough energy.
• $3 s \to 4 s$ and $3 s \to 5 s$ are forbidden, because you did not change $l$ by $\pm 1$ in one step.
• $3 s \to 3 d$ is forbidden, because $l$ changed by more than $\pm 1$ at a time. However, $3 s \to 3 p \to 3 d$ is allowed.
• $3 s \to 3 p \to 5 s$ is allowed, because you changed $l$ by $\pm 1$ each time.

Let's put this into a picture.

SODIUM ENERGY LEVEL DIAGRAM

You read this diagram by noting that the $n X$ at the top correlate with the quantum number $n$, while the single digits below each $n X$ at the top indicate what value of $n$ belongs to the orbital. For example, column $2$ for orbital "$4$" is the $4 p$ orbital.

The energy on the left is in $\text{eV}$, where $\text{1 eV" = 1.602xx10^(-19) "J}$. The small numbers along each transition line is the wavelength of the transition in $\text{nm}$. For example, the wavelength of the $3 s \to 3 p$ transition is about $\text{589 nm}$.

From this diagram, you should realize that the allowed transitions up to new excited states are all diagonal.

Can you trace the excitation pathways from the examples above? You should find that the forbidden transitions are all vertical or require two diagonal steps.