AR, IR, IE

Atomic Radius, Ionic Radius, Ionization Energy

Atomic Radius

• SInce we cannot pinpoint the positions of electrons, we cannot have a boundary as there will always be a probability of an electron being there

  • Instead distance from adjacent Nuclei ( Internuclear Distance )

• Down a group --> AR increases $\because$ the # of E-levels increase

  • More Mathematically: $AR \propto N$ ( where N is the Principle Energy Level )

• Across a period --> AR decreases $\because N$stays the same & $Z$increases --> More charge --> Atoms are more grouped together.

  • More Mathematically: $AR \propto \frac{1}{Z_{eff}}$--> They are inversely Proportional

Ionic Radius

• Where as Atomic Radius notes the distance between adjacent nucleus of Neutral atoms, Ionic Radius look at Cations & Anions

• Note Cations are smaller ( greater charge ) than a stable atom

• Note Anions are larger ( greater repulsion ) than a stable atom

• One can easily see that for Isoelectrionic Cations , the one with the greater sum charge has a smaller $IR$ ( more charge attracting )

• One can easily see that for Isoelectrionic Anions, the one with the least sum charge has a bigger $IR$( More charge repelling )

Ionization Energy

• Mole ( mol ) is an SL unit used to measure the amount of any substance: Typically used to measure large quantities of tiny entities like Atoms, Molecules, and particles. here for true definition ( IMPORTANT ).

• $1 mol = 6.02214076 * 10^{23}$ or $N_A$ Avogadro's number

• First Ionization Energies ( $IE_1$) are a way to measure the attraction between the nucleus & the outer electron.

  • More precisely its the amount of Energy to completely remove an electron from an neutral atom

  • From this we can find some trends

  
• Down a group --> Increased distance from Nucleus to Valence

  • IE becomes smaller

  • More Mathematically: $N \propto \frac{1}{IE}$

• Across a period --> $Z$increases $\therefore$ charge increases

  • IE becomes bigger

  • More Mathematically: $Z_{eff} \propto IE$

• Looking at the graph of Ionization Energies amongst the Elements, we can find evidence of why the First Energy Level has maximum of $2 e^-1$, evidence why s-orbitals contain only 2 electrons, etc..

Screening Effect and Effective Nuclear Charge

• $Z_{eff} = Z - S$--> Approximate the attractive force Valence Electrons "Feel" from nucleus

With $Z_{eff}$ being the Effective Nuclear Charge.

With $Z$ being the Nuclear Charge ( # of protons )

• They are tightly packed --> so act as one large charge

With $S$ being the # of Core Electrons , that block/shield the valence electrons

Electrons in Atoms

• Lyman's Series --> From $N\geq 2 \rightarrow N=1$( UV )

  • The elements $H$and $He$ have ground states at $N = 1$ ( why ? )

• Balmar Series --> From $N \geq 3 \rightarrow N = 2$ ( Visible )

• Paschen's Series --> From $N \geq 4 \rightarrow N = 3$

• Brackett Series --> From $N \geq 5 \rightarrow N = 4$

• Since the Energy Levels get closer and closer as N converges to $\infin$, eventually being so insignificantly close that it forms a continuum . Once reached there, the atom becomes an ion.

Calculating IE from Spectral Frequency

Goal: Relate Frequency & Energy

$\therefore$ we use the following equations

1. $c = f \lambda$ where c = $3.00 \times 10^8$ m/s

2. $E= hf$

We can now relate to result in the equation:

$$E = \frac{hc}{\lambda}$$

However note that IE is the amount of energy needed to remove 1 mole of $e^-$ from 1 mole of a gas $\therefore$ we must multiply by $N_A$, Avogadro's Number. For convention, one must turn $J$ into $kJ$ for $\frac{kJ}{mol}$

IE can be calculated from wavelength or frequency that corresponds to the energy of the electron transition.

$1 eV = 1.602 \times 10^{-19} J$