Chem chp6 equations and rules/theories

What is the relationship between wavelength and frequency of light?

c=λν

How do you calculate the frequency from wavelength?

ν=c/λ

How do you calculate the wavelength from frequency?

λ=c/ν

How do you calculate the energy of a photon from its frequency?

E=hν

How do you calculate the energy of a photon from its wavelength?

E=hc/λ

c constant

3.00 × 10 ^8

Rydberg formula for hydrogen spectral lines (wavelength)?

λ1​=RH​(1/(n1​)²−1/(n2​)²)

Rh constant

1.097 × 10^7

Energy change for a hydrogen electron transition

ΔE=−2.178×10A^−18(1/(nf)² -1/(ni)²)

de Broglie wavelength of a particle

λ=h/mv (mass and velocity)​

l number meanings

0=s, 1=p, 3=d, 4=f

Photoelectric Effect

Electrons are ejected from a metal surface when light of sufficient frequency shines on it.

Planck’s Hypothesis

Energy is quantized

Heisenberg Uncertainty Principle

You cannot know both the exact position and momentum of a particle simultaneously.

Bohr Model of the Atom

Electrons occupy quantized orbits around the nucleus.

Principal Quantum Number (n):

• Determines energy level and size of orbital.

• Values: n=1,2,3,…n = 1,2,3,\dotsn=1,2,3,

Azimuthal Quantum Number (l)

• Determines orbital shape.

• Values: l=0,1,2,...,n−1l = 0, 1, 2, ..., n-1l=0,1,2,...,n−1

• Labels: s=0, p=1, d=2, f=3

Magnetic Quantum Number (m_l):

• Determines orbital orientation.

• Values: −l→+l-l \to +l−l→+l

Spin Quantum Number (m_s):

• Determines electron spin.

• Values: +12+\frac12+21​ or −12-\frac12−21​

Pauli Exclusion Principle

No two electrons in an atom can have the same set of 4 quantum numbers.

Hund’s Rule

Electrons occupy degenerate orbitals singly first with parallel spins before pairing.

Aufbau Principle

• Electrons fill orbitals starting with the lowest energy first:

1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p

Degenerate Orbitals

• Orbitals with the same energy in a given shell.

• In hydrogen (one-electron system), all orbitals with same nnn are degenerate.

• In many-electron atoms, degeneracy depends on n and l.

Hydrogen emission

Electron falls to a lower nnn level, emitting light.

Hydrogen absorption

Electron jumps to a higher nnn level

Atomic radius

• Trend Across a Period: Decreases → More protons, same shielding → electrons pulled closer.

• Trend Down a Group: Increases → More electron shells → outer electrons farther.

Ionization Energy (IE)

• Definition: Energy required to remove an electron from a neutral atom.

• Trend Across a Period: Increases → Higher nuclear charge, electrons harder to remove.

• Trend Down a Group: Decreases → Outer electrons farther from nucleus, easier to remove.

Electron Affinity (EA)

• Trend Across a Period: More negative (exothermic) → atoms more eager to gain electrons.

• Trend Down a Group: Less negative (less exothermic) → electrons added farther from nucleus, less attraction.

Electronegativity (χ)

• Trend Across a Period: Increases → More nuclear charge, stronger pull on shared electrons.

• Trend Down a Group: Decreases → More shells → electron is farther away, less pull

Metallic vs Nonmetallic Character

• Metals: Lose electrons easily → low IE, large atomic radius.

• Nonmetals: Gain electrons easily → high IE, small atomic radius.

Removing an electron requires energy, so ΔE > 0

endothermic

Adding an electron releases energy, so ΔE < 0

exothermic