Ch. 7 Outline : Atomic Structure and Periodicity

AP Chemistry Mr. Ferwerda, Tecumseh HS 02/18/09

Ch. 7 Outline : Atomic Structure and Periodicity

A. Atomic structure and periodicity(need good chart of e-m spectrum)

1. Electromagnetic radiation

a. a form of radiant energy

b. three properties of waves

- wavelength (l - Greek lambda) (shorter wavelength = higher energy)

- frequency (v - Greek nu) (Hz - 1/s or s-1)

- speed (c)- equal for all kinds of e-m radiation ( = 2.9979 x 108 m/s)

c. lv = c (wavelength and frequency are inversely related)

_____ (T/F) The higher the frequency, the longer the wavelength.

_____ (T/F) Frequency and wavelength are inversely related to each other.

Example: Calculate the wavelength of a 99.5 MHz frequency given off by a radio station.

2. Nature of matter

a. Planck - energy is quantized DE = nhv (n = integer, h = Planck's constant 6.626 x 10-34 J x s)

- energy increases with increased frequency (decreased wavelength)

_____ (T/F) Planck determined that atoms can absorb or emit any amount of energy.

b. quantum - a small "packet" of energy - a discrete, yet varying amount (not all quanta are the same)

c. Einstein - photons (packets of light energy) are quantized (Ephoton = hv = hc/l) v = c/l

d. Einstein : E = mc2

e. dual nature of light/matter

- diffraction (scattering of light from a regular array of lines or points)- property of waves - photoelectric effect- evidence of particle nature

Example: Calculate the energy of a single photon and of a mole of photons emitted from a mercury vapor lamp with light of a wavelength of 404.7 nm.

Example 2 : The ionization energy of gold is 890.1 kJ/mol. Is light with a wavelength of 225 nm capable of ionizing a gold atom in the gas phase ?

f. de Broglie's equation : l= h/mv (where m = mass (in kg) and v = velocity in m/s)

Light has a dual nature, what about other forms of matter? (Yes)

e.g. What is the wavelength of an electron moving at 50.% of the speed of light?

3. The atomic spectrum of hydrogen

a. Contrast to a continuous spectrum - all wavelengths

b. emission spectrum of hydrogen -pattern of light emitted from an excited hydrogen atom) - a line spectrum- indicates quantized nature of hydrogen (only certain wavelengths absorbed or emitted)

How many electron transitions can take place for a hydrogen atom with an excited electron at n = 6?

4. The Bohr model - quantum model

a. energy levels available : E = -2.178 x 10-18 J(Z2/n2)

- Z = nuclear charge (number of protons)(=1 for hydrogen atom)

- n = integer- corresponds to energy levels

- neg. sign indicates negative energy (e- is bound to nucleus therefore has lower energy than free e- where n = ¥)

- J is joules

b. ground state lowest possible energy state

c. calculation of energy of quantization in hydrogen for change in energy : DE = Ef - Ei (e.g. change in E when electron moves from n = 6 to n = 5)

- positive sign indicates E (light) absorbed

- negative sign indicates E (light) emitted

d. calculation of change in electron energies DE= -2.178 x 10-18 J(1/nfinal2 - 1/ninitial2)

e. spectral transition diagram : ("spectral" because light is usually absorbed or emitted)

e. failure of Bohr model in other elements -the Bohr model did not hold true for polyelectronic atoms

_____(T/F) The Bohr model worked for all atoms of all elements.

______and ______said that electrons bound to nuclei acted as standing waves.

5. Quantum Mechanical Model of atom

a. Heisenberg, Schrodinger, de Broglie - developed wave , or quantum mechanics

- bound electron is a standing wave

- only certain circumferences will allow whole numbers of half waves

- Schrodinger's equation HΨ = EΨ

- Ψ- wave function, or "orbital" (function of coordinates x, y and z)( does not indicate pathway of electron)

- H - operator - contains mathematical terms which produce total energy of the atom

- E - total energy of atom (kinetic and potential)

- a specific wave function is an orbital

An ______is a specific wave function.

The ______uncertainty principle states that we can not know both the position and the momentum of an electron.

b. Heisenberg uncertainty principle-cannot know both momentum and position of electron at a given time

c. Physical meaning of wave function in light of uncertainty principle : probability of e- location

- probability distribution- represents square of wave function - produces an e- density map

- radial probability distribution - total probability within spherical shells

- orbital - no definite size-defined as area in which 90% of total e- probability

6. Quantum numbers-describe orbitals

a. Principal quantum number (n = 1, 2, 3, ...)

- indicates size and energy of orbital (higher n, higher energy-less bound, less neg. energy)

for n = 1,

n = 2,

n = 3,

n = 4,

b. Angular momentum number (azimuthal quantum number) (l)

- integral values from 0 to n-1

- indicates shape of orbital (l = 0 = s; l = 1 = p; l = 2 = d; l = 3 = f )

for l = 0, ml =

for l = 0, ml =

for l = 0, ml =

for l = 0, ml =

c. magnetic quantum number (ml)

- integral values from l to - l including 0

- indicates position of orbital in space relative to other orbitals

d. Spin quantum number (ms) - indicates rotation of electron

- -½ or -½

Table 7-1 : Quantum numbers for first four energy levels

* The 3 p orbitals are x, y, and z (e.g. 2px, 2py, 2pz)

** The 5 d orbitals are xz, yz, xy, x2-y2, and the z2 (e.g. 3dxz, 3dyz, 3dxy, 3dx2-y2, and the 3dz2)

Sample problems :

1. Which of the following sets are incorrect?

a. n = 2, l = 2, ml = -1

b. n = 3, l = 2, ml = -3

c. n = 4, l = 2, ml = -1

2. How many electrons can have the quantum numbers n = 5, ml = +1?

3. How many orbitals can have the designation n = 3?

4. How many electrons can have the designation n = 3?

7. Orbital shapes and energies

a. nodal surface (nodes)- regions of zero probability of finding an e-

b. hydrogen atom - orbitals in energy levels (same n value) are degenerate - have the same energy

8. Electron Spin and the Pauli Principle

a. Pauli exclusion principle - in a given atom, no two electrons can have the same set of four

quantum numbers (i.e. -only two electrons per orbital)

9. Polyelectronic atoms

a. three forces affecting distribution of electrons

- kinetic energy of electrons (outward)

- potential energy of attraction of nucleus (inward)

- potential energy of repulsion of electrons

b. electron correlation problem-since paths of electrons cannot be known exactly, repulsions cannot be calculated exactly- must make approximations

c. shielding - inner electrons shield outer electrons from nuclear charge (held less tightly)

d. orbitals in polyelectronic atoms are not degenerate (s < p < d < f)

e. penetration effect -ex. In general, 2p electrons are closer to the nucleus and therefore have a lower energy than 2s, however, 2s electrons spend a small, but significant amount of time closer to the nucleus and are said to "penetrate" and thus are considered to have a lower energy state and are filled first

d. Electron configuration problems

Rules governing electron configurations :

- Aufbau rule

- Hund's rule

- Pauli exclusion principle

Write the orbital electron configuration of calcium, and then give its summary electron configuration.

Summary :

What is the summary electron configuration of yttrium? (at. no. 39)?

Sample problems :

1. What is the electron configuration of neon?

2. What is the electron configuration of chromium ?

3. What is the identity of the element with the electron configuration 1s22s22p63s13p1 in an excited state ?

4. Write the electron configuration for the following orbital notation for an atom with 8 protons, identify the species (atom, ion etc) and write its formula .

5. How many unpaired electrons are found in nitrogen in its ground state?

6. Give a set of values for the four quantum numbers of the valence electrons of phosphorus in its ground state.

Write the summary electron configuration for the element zinc.

Electron configuration of tin (at. no. 50)?

Electron configuration of osmium (at. no. 76)?

Write the summary electron configuration for chromium :

_____ (T/F) Phosphorus is paramagnetic.

_____ (T/F) Phosphorus can form the compound PF5.

The following shows an element in its ground state. Is this a metal or nonmetal?

Characteristics of this element?

have luster or nonlustrous?

conductor or insulator?

relatively high or low melting point?

electropositive or electronegative?

state?

10. History of periodic table

a. Mendeleev given most of the credit because of his emphasis on using it as a tool to predict yet unknown elements.

11. Aufbau ("building up") principle and the periodic table

a. Aufbau principle - as protons are added to successive atoms of elements, so are electrons

b. Hund's rule - the lowest energy configuration for an atom is the one having the most unpaired electrons allowed by the Pauli principle in degenerate orbitals

c. Valence electrons - electrons in the outermost principal quantum energy level of an atom

d. core electrons - "inner" electrons

e. configurations of representative elements vs. transition metals and inner transition metals (lanthanides and actinides)

f. exceptions to expected configurations - chromium [Ar] 4s13d5 and copper [Ar] 4s13d10

g. arrangement of periodic table- representative elements, transition metals, lanthanides, actinides, s block, p block, d block and f block

h. IUPAC periodic table- numbers Groups 1-18 instead of 1A-8A and "B" designation for transition metals

i. determination of electron configurations

12. Periodic trends in atomic properties

a. major factors affecting trends

- nuclear charge - increases across a period causing a greater attraction for electrons

- shielding - additional energy levels down a group causes a decrease in the attraction of the nucleus for the outermost electrons

- electron configuration - most important - groups have similar electron configurations giving them similar chemical and physical properties

a. ionization energy- the energy needed to remove an electron from a gaseous atom (X(g) -->X+(g) + e-) in its ground state

- first ionization energy (I1)- energy needed to remove the first electron

- second ionization energy (I2) - energy needed to remove second electron

- note pattern in aluminum [Ne]3s23p1

I1- removes p1electron = 580 kJ/mol

I2 removes one 3s electron = 1815 kJ/mol - higher due to positive charge on Al+ ion

I3 removes remaining 3s electron = 2740 kJ/mol (Al2+ )

I4 removes core 2p electron = 11,600kJ/mol - core electrons come from stable noble gas configuration

- periodic trend is for ionization energy to increase across a period - increased nuclear charge with no increase in shielding

-exceptions-due to electron repulsion i.e. nitrogen and oxygen

N : O : - easier to remove outer 2p electron from oxygen than nitrogen because of doubly occupied 2porbital

-group trend is to decrease down a group - increased shielding, outer electrons are farther from nucleus

b. electron affinity - the energy change associated with the addition of an electron to a gaseous atom : X(g) + e- ---> X- (g)

- sign of energy change- negative if exothermic, positive if endothermic

- periodic trend - negative electron affinities increase across a period (more energy released)

- exceptions : carbon has a negative electron affinity (becomes more stable) and nitrogen has a positive electron affinity (becomes unstable- higher energy)

C : N : - an electron added to carbon goes into an empty orbital whereas an electron added to nitrogen goes into an occupied orbital resulting in electron repulsion

- Group trend - electron affinities become more positive (less negative) because less energy is released due to shielding and increased distance from nucleus (less attraction for e-)