Ch. 7 Atomic Structure and Periodicity

7.1 Electromagnetic Radiation

I. Waves• A. Energy travels via electromagnetic radiation

(light) with wave-like nature

• B. Wavelength (): distance between two crests (highest point) or troughs (lowest point), in meters

II. Frequency• A. Frequency (): # of wave cycles per second

passing given point (units are Hertz (1/second))

2 cycles per second = 2 Hertz (2 Hz)

3 cycles per second = 3 Hertz (3 Hz)

Longer wavelength = lower frequency

• A. Speed of light is a constant (C) = • • B. C = 3.00 x 108 m/s

• C. Different forms of light have different energy, wavelength

III. Types of E.R.

7.2: I. Nature of Matter• A. Was thought light only moved in waves so they

have continuous amounts of energy• B. Found that energy can be lost in whole number

multiples (h). • C. Planck’s constant (h) = 6.626x10-34 J•sec• D. “Quantized”: light travels in packets of energy

(“Quantum”)

II. Photons of Energy• A. Photons: electromagnetic particles

• B. Ephoton = h = hC/

• C. E = mC2

III. Duality of Light• A. Light can exist as wave and particle simultaneously• B. Determined through a double slit experiment

IV. De Broglie• A. De Broglie’s Eqn: found that particles of all

material can exhibit wave-like properties• B. = h/mV, where V is velocity• C. Large objects act as mostly particles • D. Small objects, mostly waves (light)

• E. Intermediate objects exhibit equal amounts of both (ex. Electrons)

V. Diffraction• A. Diffraction: scattering of light when light is

bent by a medium (ex. Through prism)

• B. Diffraction pattern: light scattered as it’s passed through a crystalline molecule due to light interference (ex. NaCl)

7.3: I. Atomic Spectrum of Hydrogen• A. H2 gives off light when given energy

• B. Line spectrum: only color wavelengths that are emitted are visible

• C. ***Shows that only certain wavelengths of energy are present in certain elements***

• D. Reinforces “quantized” energy of light

7.4: I. The Bohr Model• A. Bohr thought that electrons move around

the nucleus in certain allowed circular orbits• B. Believed that electrons could only inhabit these fixed orbits when gaining or losing energy (cannot be in-between)

• C. Derived calculation to determine energy levels

• D. E = 2.18x10-18 J (Z2/n2)

• E. Z = nuclear charge, n = integer for orbit #

• F. If we calculate the energy associated with different orbits for Hydrogen e-s, we get this chart

• G. Notice that higher orbital levels have more energy (Potential)

• H. The “ground state” is the most stable

• I. Returning to the ground state from higher levels releases extra energy as photons of light

II. In Reality…• A. Bohr’s model only works for Hydrogen

• B. In fact, electron orbits are not all circular

• C. This model was important though in the formulation of further theories

7.5: I. Quantum Mechanical Model• A. Schrödinger and DeBroglie focused on wave

nature of electrons• B. Related motion of electrons to standing waves• C. Nodes: fixed points of waves• D. Antinodes: area of maximum movement• E. Wave function: represents location of electron

in 3-D space (“Schrödinger equation”)• F. Orbital: any possible solution of the wave

function, where electrons can actually exist

II. Heisenberg Uncertainty Principle• A. States that we cannot know the position and

the momentum of a particle at a given time

• B. We cannot figure out how the electron is moving around the nucleus in its possible positions, but we can mathematically determine that they are

• C. ∆x • ∆(mV) ≥ h/4• D. ∆x = a particles uncertainty, V is velocity, m in kilograms

• E. The more accurately we know an electron’s position, the less accurately we know its momentum

• F. Only significant for small particles

• G. Can’t assume we know how the electrons are traveling around the nucleus

III. Physical Meaning of Wave Function

• A. The square of the wave function is the probability of finding an electron near a point in space

• B. We determine electron locations by probability distribution or electron density mapping

• C. This is the first orbital of Hydrogen called “1s”

7.6: I. Quantum Numbers• A. Describe various properties of the orbitals

electrons can inhabit• B. Principal Quantum Number (n): whole

number values, relate to size and energy of orbital

• C. Higher n values mean larger orbitals (farther from nucleus), higher energy

• D. Angular Momentum Quantum Number (ℓ): has values from 0 to n-1 for each Principal Quantum #, describes shape of orbital (represented by letters for different shapes)

• E. Magnetic Quantum Number (mℓ): values between ℓ and -ℓ including 0

• F. Electron Spin Quantum Number (ms): indicate two directions electrons can spin (+1/2, -1/2), both exist for each orbital

7.7: I. Orbital Shapes and Energies• A. Shapes of s,p,d,f

orbitals are best illustrated by electron probability diagram

• B. Like a standing wave, orbitals have nodes and antinodes, nodes are fixed parts (no electrons), antinodes are where electrons can exist

II. S Orbitals• A. Each level up has one extra area for electrons to inhabit

• B. Each antinode of this orbital can hold up to 2 electrons

III. P Orbitals• A. Figure-8 shaped

along x, y, and z axis

• B. Node exists between two lobes

• C. Each orbital contains two electrons (6 total)

• D. Starts at Quantum level 2

• E. Each orientation named after axis it goes along

Ex. 2px, 2py, 2pz

IV. D Orbitals• A. Has 5 orientations (“clover-leaf”) each

holding 2 electrons (10 total)• B. Starts at n = 3

• A. Start at n=4, contain 7 orientations, each holding two electrons (14 total)

V. F Orbitals

7.8: I. Electron Spin and Pauli Principle• A. Magnetism is caused by moving charges

• B. It was observed that electrons can have two possible magnetic states meaning that electrons can spin in one of two directions

C. Pauli Exclusion Principle says since all quantum states cannot be identical for two electrons, spin state must be different for electrons in same orbital

7.9: I. Polyelectronic Atoms• A. In atoms with more than one electron (all but

Hydrogen) need to consider repulsion between electrons to determine energy of electrons

• B. Need to treat each electron like it is moving as a result of nuclear charge and the average repulsion of other electrons

• C. Electrons are easier to remove if there is electron repulsion because the positive nuclear charge won’t have as much influence on attraction

II. “Effective Nuclear Charge”• A. Zeff = Zactual – effect of electron repulsion• B. Z is the number of protons• C. Zeff can be plugged into the Bohr equation

replacing Z• D. We need to treat each electron separately to

determine overall effect of nuclear charge

7.10: I. History of the Periodic Table• A. Mendeleev is one of two people to

independently devise early periodic table• B. Was organized based on element properties

and atomic mass• C. Predicted placement of some unknown elements

• D. Current P.T. based on properties and atomic number

7.11: I. Aufbau Principle • A. Electrons are added to different electron

orbitals as they are added to atoms

• B. Orbital Diagram: shows placement of electrons in orbitals

• C. Rules: 1. Electron order based on energy of orbitals (relates to order of periodic table)

2. S orbitals have one orbital (2 e-s)

P orbitals have 3 orbitals (6 e-s)

D orbitals have 5 orbitals (10 e-s)

F orbitals have 7 orbitals (14 e-s)

Orbital Order Cheat Sheet• 7 s 7p 7d 7f

6s 6p 6d 6f

5s 5p 5d 5f

4s 4p 4d 4f

3s 3p 3d

2s 2p

1s

Or follow order from P.T.

Orbital Diagram Rules Continued…• 3. “Hund’s Rule”: lowest energy state is when

electrons are unpaired in orbital groups before paired

4. Different electron spins are shown by up/down arrows

• D. Ex. Carbon 1s 2s 2p • E. Also can write as: 1s2 2s2 2p2

• F. Noble Gas Shortcut: [He] 2s2 2p2

• G. Valence electrons: electrons in outermost principle quantum level

• H. Ex. Carbon valence e-s are 2s and 2p (4 valence e-s)

• I. Core electrons: innermost electrons

• J. Important Trend of P.T.: elements in same group have same # of valence e-s

• K. Unique e- configurations: Cr, Cu

• L. Chromium should be: [Ar] 4s2 3d4

Actually: [Ar] 4s1 3d5

• M. Copper should be: [Ar] 4s2 3d9

Actually: [Ar] 4s1 3d10

7.12: I. Development of Polyelectronic Model

• A. Ionization energy equation based on Bohr’s model multiplied by Avogadro’s number to determine J/mole or KJ/mole

• B. Eionization = 1.31x106J/mole(z2/n2) or

= 1310 kJ/mole(z2/n2)

• C. We can also calculate the value for the effective nuclear charge Zeff by plugging in values and solving for it in Bohr’s equation or ionization equation

Sample Calc. of Zeff

• Eion for Na = 1.39x105 KJ/mole

• Plug into Bohr or Eion equation, to solve for Zeff for n = 1

• Eion = 1310 KJ/mole (Zeff2/n2)

• 1.39x105 KJ/mole = 1310 KJ/mole (Zeff2/12)

• Zeff2 = 1.39x105 KJ/mole / 1310 KJ/mole

• Zeff2 = 1.06x102

• Zeff = 10.3

II. Interpretation of Zeff values• A. For Sodium, the actual Z value is 11

because of the number of protons, yet there is less of an effective charge (10.3) because of the electron repulsion

• B. If we calculate the n=3 Zeff for Sodium you get 1.84 meaning that the farther you get from the nucleus, the less the effect of the charge of the nucleus on electrons (which should make sense)

• C. The inner electrons “Shield” the outer electrons from the effect of the nuclear charge

7.13: I. Periodic Trends in Atomic Properties

• A. Ionization Energy: energy required to remove an electron from an atom or ion that are in their ground state

• B. First electron to be removed is highest energy one because it needs least energy to escape

• C. First ionization energy: energy to remove first electron

• D. Second ionization energy is always higher

II. Eionization Rationalization• A. As e- removed atomic charge increases and

holds e- more strongly• B. Valence e- easier to remove than core e-

because of shielding• C. On P.T.: 1st Eionization increases as you go left

to right and Bottom to top• D. Left to right because increasing protons

have more attractive force than e- shielding• E. Bottom to top because bottom atoms have

farther out orbitals, less nuclear attraction

III. Electron Affinity

• C. Ex. Carbon has 2 unpaired 2p e-s, so it can take in one more without pairing them, but Nitrogen has 3 unpaired 2p e-s and would have to pair them to become -1 so it releases more energy

• D. No particular trend seen up or down because you still have similar repulsive forces for groups

• A. Energy change when adding an e-

• B. Increase left to right due to repulsion of e- by pairing them

IV. Atomic Radius• A. Increase from right to left (increased nuclear

charge pulls electrons closer)

• B. Increase top to bottom (adding more orbital shells)

V. Summary of Periodic TrendsIncreasing ionization energy, electron affinity

Increasing atomic radii

Increasing atomic radii, decreasing ionization energy

VI. Properties of Metals• A. Metals found on left of table, low ionization

energies, form positive ions by giving up e-

• B. Non-metals on right of table, high ionization energies, form anions when adding electrons

• C. Metalloids or semi-metals: have both metallic and non-metallic properties based on conditions

VII. Alkali Metals• A. Li, Na, K, Rb, Cs, and Fr most chemically

reactive of all metals

• B. Hydrogen too small to act as metal because single electron bound so tightly to nucleus

• C. Low ionization energies allow e- to be lost easily

• D. Hydration energy: energy released when water attached

• E. Lithium has most because it is small; less shielding effect of e-; more effective nuclear charge for water to grab onto (called “charge density”)