#### Related to [[Atomic structure]] and [[Quantum mechanics]] --- ## Definition - An atomic orbital is a mathematical term in atomic theory and quantum mechanics that describes the **position** of electrons around an atom. --- ## The basics - An element's electrons fill orbitals in the order of the below picture. Each *letter or subshell* can fit a different number of electrons. - Each orbital must have at least 2 electrons in it, one represented by an up arrow and one represented by a downwards facing arrow. - The reason for this representation is to illustrate that fact that **orbitals can only hold two electrons that have opposite spins**, This is because the **Pauli exclusion principle** wont allow overlapping electrons. - An electrons **spin** is the direction the electron "faces" or the direction it is spinning. > [!quote] > > ##### **What order are orbitals filled in?** > > ![[Orbitals 2.png]] > ##### **What do the letters stand for?** > > ![[Term chart orbitals.png]] > ##### **How many electrons can each subshell hold? NOTE: all orbitals fill up FULLY with up spin electrons before filling up with down spin electrons. Also, each box is known as a *degenerate orbital*.** > > ![[Orbitals subshells.png]] >- The **ground state configuration** means that the electrons fill up the subshells in the order given above starting with 1s. >- An **excited state configuration** means that the electrons get *bumped up* one subshell and start at the *2s* subshell. --- ## Special rules regarding orbitals - Orbitals are most stable when they are either **fully filled or exactly half filled**. Copper and Chromium **ONLY** take this consideration into account. - As a result electrons may move **up** from an **s subshell to another partially filled subshell if it results in that subshell being exactly half filled or fully filled.** ### THE FOLLOWING ONLY HAPPENS IN COPPER AND CHROMIUM >[! Copper's electron configuration as an example:] > >![[Orbitals copper.png]] ## Spatial arrangement - This is represented by the letter m. It represents the orientation of the orbital or which axis it is on. As you can see each orbital shape has different configurations which are dictated by the spatial arrangement of that orbital. - The spatial arrangement ranges from (n-1) in both the **negative and positive direction INCLUDING 0**. >[!quote] ><br> > >![[Pasted image 20230117125145.png | 700]] ## Shorthand arrangement - To make the full electron config arrangement smaller people often list the Nobel gas from the row above a specified element and include only the subshells after that Nobel gas *(ex: [Ar]4s2)*. - The reason why the d subshell is listed before the s one in the image below is because 3 comes before 4. **Remember that subshells should be listed in n order only in the shorthand arrangement.** >[!quote] ><br> > >![[short electron config.png]] --- ## The shape of orbitals - Since [[Electrons]] want to be as far away from all other electrons as possible. The shape and position of the orbitals around a nuclei change as more electrons are added and fill different **subshells**. - The shape of orbitals are also related to an [[Electrons]] **wave function**. Since its impossible to know the exact location of an electron an any given time due to **Hinesburg's uncertainty principle** *(see [[Quantum mechanics]] for more info)*. The shape of orbitals are governed by the **probability** of an electron being there (which is given by the **square wave function**). > [! How the shape of orbitals relates to an electron's wave function] > <br> > > ![[Orbitals relation to wave function.png]] ### Signs of orbitals - The S orbital is positively charged at **all points in space** however the **P and D** orbitals all have different "areas" where they are positively charged and negatively charged. - Also, like the S orbital **F orbitals are positively charged everywhere.** >[!quote] ><br> > >- **P orbitals:** > ><br> > >![[P orbitals.png]] > >- **D orbitals:** > >![[d orbitals.png]] > >- **F orbitals:** > >![[f orbitals.png]] --- ## Energy of orbitals - The **primary quantum number** also denoted as *n* *generally* represents the *energy* of a given orbital. - P orbitals are at a higher energy level then s orbitals and d orbitals have more energy then p orbitals and so on... - [[Polyelectronic Atoms]] **past hydrogen have their P, D and F sublevels shifted up to have higher energy which makes it difficult to determine the relative energy level of orbitals as you can see in the image below.** > [!quote] > <br> > > ![[Pasted image 20230118124248.png]] --- ## Electron shielding - Electron shielding is the process by which electrons *protect* electrons usually in the [[Valence Electrons|valence ring]] from the strong **positive** charge of the nucleus. >[!tip] >- In general going **across a period from left to right** increases the number of electrons and thus increases the strength of thier shielding even though they may still be in the valence shell. >- Also **bigger atoms** have greater shielding. - In general **electrons that are closest to the nucleus provide the greatest shielding.** The closer an electron is to the nucleus the more it shields other electrons that are further *away* from the nucleus. - Remember that electrons are held to the nucleus by the [[Nuclear force]]. >[!quote] >##### Shielding example ><br> > >![[electronshielding2.png|800]] >[!quote] >## Effective nuclear charge >- The effective nuclear charge of an atom is **the attractive positive charge of nuclear protons acting on valence electrons**. Electrons shielding an atom's nucleus will push against other electrons preventing any one electron from experiencing the nuclei's *maximum nuclear charge*. >- Effective nuclear charge **increases towards the top left of the periodic table** since those atoms have the smallest size and a few other factors. >- See [[Orbitals]] for more. ></br> > >![[shielding math.png|825]] --- #mainpage