Atomic Structure: Orbitals, Configurations, and Quantum Numbers

Flashcards covering atomic orbitals, electron configurations, paramagnetic/diamagnetic properties, quantum numbers, electronic filling rules, and atomic nodes based on lecture notes.

How is an atomic orbital defined in the 3D model of the atom?

A 3-Dimensional area (space) around the nucleus in which the probability of finding an electron is maximum (up to $95\%$).

What are the shapes and number of orbitals for the s, p, and d subshells?

s: Spherical (1 orbital); p: Dumb-bell (3 orbitals: $p_x$, $p_y$, $p_z$); d: Double-dumbell (5 orbitals: $d_{xy}$, $d_{yz}$, $d_{xz}$, $d_{x^2-y^2}$, $d_{z^2}$).

What is the ground state electron configuration and number of unpaired electrons for Nitrogen ($Z=7$)?

Configuration: $1s^2 2s^2 2p^3$; It has 3 unpaired electrons (Paramagnetic).

What is the result of an element having unpaired electrons regarding its magnetic properties?

Elements with unpaired electrons are attracted by external magnetic fields, called PARA MAGNETIC, and are typically colored.

What characterizes DIA MAGNETIC substances?

They do not contain unpaired electrons (all electrons are paired), are repelled by external magnetic fields, and are typically colorless.

Why are the electron configurations of Chromium ($Z=24$) and Copper ($Z=29$) considered exceptions?

Chromium is $[Ar] 4s^1 3d^5$ and Copper is $[Ar] 4s^1 3d^{10}$; these occur because exactly half-filled and fully-filled orbitals are more stable.

What are the specific conditions for the orbital configuration exceptions observed in elements like $Cr$ and $Cu$?

The orbitals must be close in energy ($4s, 3d$ or $5s, 4d$), the atom should be neutral, and only 1 electron should be transferred from the s-orbital to the d-orbital.

What is the rule for writing the electron configuration of a cation?

Never write the configuration directly; first write the configuration of the neutral atom, then remove electrons from the outermost shell (the highest $n$ value) last.

How many unpaired electrons are in an $Fe^{2+}$ ion ($Z=26$)?

The configuration of $Fe$ is $[Ar] 4s^2 3d^6$. For $Fe^{2+}$, the two $4s$ electrons are removed, leaving $[Ar] 3d^6$, which contains 4 unpaired electrons.

What information does the Principal Quantum Number ($n$) provide?

It tells about the shell number to which the electron belongs (also known as the building number).

What are the fixed values of the Azimuthal Quantum Number ($l$) for s, p, d, and f subshells?

s: $l=0$; p: $l=1$; d: $l=2$; f: $l=3$. This number indicates the floor inside the shell.

How is the Magnetic Quantum Number ($m_l$) calculated, and what does it represent?

It tells about the number of orbitals present in a given subshell; for each value of $l$, $m_l$ can have values from $-l$ to $+l$.

What is the formula to calculate the total number of orbitals in a shell with principal quantum number $n$?

The number of orbitals is equal to $n^2$.

State the Aufbau Principle.

In the ground state of atoms, orbitals are filled in order of their increasing energy according to the $(n+l)$ rule.

What are the two components of Pauli's Exclusion Principle?

1. An orbital can have a maximum of 2 electrons with opposite spins. 2. No two electrons in an atom can have the same set of 4 quantum numbers.

What is Hund's Rule of Maximum Multiplicity?

Electron pairing in orbitals belonging to the same subshell (p, d, or f) does not take place until each orbital is singly occupied.

Define 'Degenerated' orbitals.

Orbitals which have the same energy are called degenerated orbitals.

What is a 'Black Body' and how does its emitted light behave?

An ideal body that absorbs all frequencies of radiation and emits all frequencies when heated; the intensity and amount of light emitted depend on the temperature.

What is a 'Node' and how are the different types calculated?

A region where the probability density ($\psi^2$) of an electron is zero. Total nodes: $n-1$; Angular nodes: $l$; Radial nodes: $n-l-1$.

How many radial nodes are present in a $3p$ orbital?

For $3p$: $n=3$, $l=1$. Radial nodes = $n-l-1 = 3-1-1 = 1$.