Atomic Structure, Isotopes, Quantum Numbers, and Periodic Trends: General Chemistry Study Notes

Atomic Structure and Isotopes

Subatomic Particles and Isotope Notation

Atoms are composed of three main subatomic particles: protons, neutrons, and electrons. The number of protons defines the atomic number and the element. Isotopes are atoms of the same element with different numbers of neutrons.

• Proton (p+): Positively charged particle found in the nucleus.

• Neutron (n0): Neutral particle found in the nucleus.

• Electron (e-): Negatively charged particle found in orbitals around the nucleus.

Isotope notation: AZX, where A = mass number (protons + neutrons), Z = atomic number (protons), X = element symbol.

Isotope Symbol	Atomic Number	Mass Number	# of Protons	# of Neutrons	# of Electrons
18F	9	18	9	9	9
24Na	11	24	11	13	11
79Br	35	79	35	44	35

• Atoms are electrically neutral, so the number of protons equals the number of electrons.

• Ions have unequal numbers of protons and electrons.

Atomic Number, Mass Number, and Charge

• Atomic Number (Z): Number of protons in the nucleus.

• Mass Number (A): Total number of protons and neutrons.

• Charge of Atom: Atoms are neutral; ions have a net charge.

• Charge of Nucleus: Equal to the number of protons (positive charge).

Ions and Isotopes

Ion Table: Protons, Neutrons, and Electrons

Ions are atoms or molecules with a net electric charge due to the loss or gain of electrons.

Ion	Number of Electrons	Number of Protons	Number of Neutrons
45Sc2+	21	24	26
40Ca2+	18	20	22
17O-	10	8	9
21Ne	10	10	11

Average Atomic Mass

The average atomic mass of an element is calculated using the masses and relative abundances of its isotopes:

$\bar{A} = \sum (\text{isotope mass} \times \text{fractional abundance})$

Example (Chlorine):

• Isotopes: 35Cl (75.53%), 37Cl (24.47%)

• Calculation: $\bar{A} = 34.969 \times 0.7553 + 36.966 \times 0.2447 = 35.45$ amu

Mole Concept and Molar Mass

Avogadro's Number and Moles

The mole is a counting unit in chemistry. One mole contains Avogadro's number ($6.022 \times 10^{23}$) of particles (atoms, molecules, ions).

• Molar Mass: The mass of one mole of a substance, in grams per mole (g/mol).

• Example: Molar mass of SO3: $32.07 + 3 \times 16.00 = 80.07$ g/mol

Stoichiometry: Mass, Moles, and Atoms

• Converting grams to moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

• Converting moles to atoms: $\text{atoms} = \text{moles} \times 6.022 \times 10^{23}$

• Example: How many grams of gold in 15.3 moles? $15.3 \text{ mol} \times 197.0 \text{ g/mol} = 3014 \text{ g}$

Quantum Numbers and Electron Configuration

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the properties of electrons in orbitals.

• Principal quantum number (n): Energy level (n = 1, 2, 3, ...)

• Angular momentum quantum number (l): Subshell (l = 0 to n-1; s, p, d, f)

• Magnetic quantum number (ml): Orientation (-l to +l)

• Spin quantum number (ms): Spin (+1/2 or -1/2)

Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

Electron Configuration and Subshells

• Maximum electrons in a subshell: $2(2l+1)$

• Example: f-subshell (l=3) can hold 14 electrons.

• Impossible configurations: For example, 2d5 is not possible because d orbitals start at n=3.

Light, Energy, and Atomic Spectra

Electromagnetic Radiation and Energy Calculations

• Speed of light: $c = 3.00 \times 10^8$ m/s

• Relationship: $c = \lambda \nu$ (wavelength × frequency)

• Energy of a photon: $E = h\nu$

• Planck's constant: $h = 6.63 \times 10^{-34}$ J·s

Example: Calculate the energy of a photon with frequency $6.1 \times 10^{14}$ Hz:

$E = h\nu = (6.63 \times 10^{-34} \text{ J·s})(6.1 \times 10^{14} \text{ s}^{-1}) = 4.0 \times 10^{-19} \text{ J}$

Bohr Model and Hydrogen Atom Transitions

• Energy levels: $E_n = -2.18 \times 10^{-18} \left(\frac{1}{n^2}\right)$ J

• Energy change for transitions: $\Delta E = -2.18 \times 10^{-18} \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$ J

• Wavelength of emitted/absorbed light: $E = \frac{hc}{\lambda}$

Example: Calculate the wavelength for a transition from n=4 to n=1 in hydrogen:

$E = 2.18 \times 10^{-18} \left(\frac{1}{1^2} - \frac{1}{4^2}\right) = 2.04 \times 10^{-18}$ J

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

de Broglie Wavelength

• de Broglie equation: $\lambda = \frac{h}{mv}$

• Example: For a 2.9 g Ping-Pong ball at 27 mph, $\lambda \approx 1.89 \times 10^{-32}$ m

Periodic Trends

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion.

• Trends: Increases across a period (left to right), decreases down a group.

• Explanation: Electrons closer to the nucleus are held more tightly (less shielding).

Ionization Energy (kJ/mol)	1st	2nd	3rd	4th
Element A	578	1817	2745	11580

Large jumps in ionization energy indicate removal of a core (non-valence) electron.

Isoelectronic Species

Isoelectronic species have the same number of electrons but different nuclear charges.

• Example: F- and Na+ are isoelectronic (10 electrons each).

Summary Table: Key Formulas

Concept	Formula
Average Atomic Mass	$\bar{A} = \sum (\text{isotope mass} \times \text{fractional abundance})$
Energy of a Photon	$E = h\nu$
Speed of Light	$c = \lambda \nu$
de Broglie Wavelength	$\lambda = \frac{h}{mv}$
Bohr Energy Levels	$E_n = -2.18 \times 10^{-18} \left(\frac{1}{n^2}\right)$
Moles to Atoms	$\text{atoms} = \text{moles} \times 6.022 \times 10^{23}$

Additional info:

• Some explanations and context were expanded for clarity and completeness.

• Tables were reconstructed and formulas were provided in standard LaTeX format.