David Liu
April 11, 2005
Period 1
Chapter 7 – Atomic Structure and Periodicity
7.1 Electromagnetic Radiation
Waves – wavelength, frequency, speed
Wavelength – (lambda) distance between two consecutive peaks or troughs in a wave
Frequency – (nu) number of waves per second that pass a given point in space
- (Wavelength)(Frequency) = C (speed of light, 2.9979 · 10^8 m/s)
- Wavelength – meters, frequency – cycles per second
Gamma rays – X rays – ultraviolet – visible – infrared – microwaves - radio waves
Short -----------------------------------------------------------------------------------long
7.2 The Nature of Matter
Max Planck (1858-1947) - ▲E = nhv (n = integer, h = Planck’s constant 6.626 · 10^-34, v =
frequency of electromagnetic radiation absorbed or emitted.)
-means that energy can be gained or lost only in integer multiples of hv (energy is quantized)
Albert Einstein – electromagnetic radiation can be viewed as a stream of “particles” – photons
E (photon) = hv = hc/wavelength
E = mc^2 – energy has mass
Mass of a photon = m = E/c^2 = h/ (wavelength)C
Dual nature of light – wavelike and has properties of matter
Broglie – particle with velocity – m = h/ (wavelength)(velocity)
Wavelength = h/mv (de Broglie’s equation)
Diffraction – light is scattered from a regular array of points of lines. Colors are separated.
Can be regular arrangement of grooves or atoms/ions
All matter exhibits both particulate and wave properties
7.3 The Atomic Spectrum of Hydrogen
Continuous spectrum – white light passes through a prism, all wavelengths of visible light
Hydrogen emission spectrum – line spectrum – only see a few lines that correspond with a wavelength
-only certain energies are allowed for the electron in the hydrogen atom – quantized energy
▲E = hv = hc / (wavelength)
7.4 The Bohr Model
Niels Bohr (1885-1962) – quantum model for hydrogen
The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits
Gave hydrogen atom energy levels consistent with hydrogen emission spectrum
Energy levels available to the electron in the hydrogen atom: E = -2.178·10^-18 J(Z^2/n^2)
- n = integer, Z= nuclear charge
▲E = energy of final state – energy of initial state (for electron falling to ground state)
-wavelength of emitted photon = ▲E = h(C/wavelength) or wavelength = hc/▲E
Electron moving from one level (n initial) to another level (n final)
▲E = E final – E initial = -2.178 · 10^-18 (1/n final ^2) – (1/n initial ^2)
Bohr’s model is fundamentally incorrect because it only works applied to hydrogen
7.5 The Quantum Mechanical Model of the Atom
Heisenberg, Broglie, Schrodinger developed wave mechanics (quantum mechanics)
Wave mechanical description of the atom
Specific wave function – orbital – don’t know how the electrons are moving in an orbital
Heisenberg’s uncertainty principle – there is a fundamental limitation to just how precisely we can know
both the position and momentum of a particle at a given time - ▲x·▲(mv) ≥ h/4 (pi)
▲x is uncertainty in particle’s position, ▲mv is uncertainty in particle’s momentum, h = Planck’s constant
Probability distribution – intensity of color used to indicate the probability value near a given point in space
-electron density map (electron probability, electron density)
Radial probability distribution – total prob. Of finding the electron in each spherical shell is plotted vs. the
distance from the nucleus.
The definition most often used by chemists to describe the size of the hydrogen 1s orbital is the radius of
the sphere that encloses 90% of the total electron probability.
7.6 Quantum Numbers
Principal quantum numbers (n) – integral values (1,2,3…) Related to the size and energy of the orbital. As
n increases, orbital becomes larger, electron spends more time further away from the nucleus.
Increase in n, higher energy.
Angular momentum quantum number (l) - values 0 to (n-1) for each value of n. Related to shape of atomic
orbital. Commonly assigned a letter. l = 0 is s. l = 1 is p. l = 2 is d. l = 3 is f.
Magnetic quantum number (ml) integral values between l and – l. Related to the orientation of the orbital in
space relative to the other orbitals in the atom.
7.7 Orbital Shapes and Energies
Nodal surfaces (nodes) - areas of zero probability of an electron. As n increases, number nodes increases.
S orbital – spherical shape
2P orbital – have two lobes separated by a node at the nucleus
3d orbital – four lobes centered in the plane indicated in the orbital label or 2 lobes along the z axis
and a belt centered on the xy plane
4f orbital – very complex, see diagrams
Degenerate orbitals – orbitals with the same value of n, thus having the same energy
Ground state – electron resides in 1s orbital
Excited state – electron transferred to a higher-energy orbital
7.8 Electron Spin and the Pauli Principle
Electron spin – electrons can have two spin states which produce two opposite magnetic moments
Electron spin quantum number - +1/2 or -1/2
Pauli exclusion principle – in a given atom no two electrons can have the same set of four quantum
numbers
An orbital can only hold two electrons, and they must have opposite spins
7.9 Polyelectronic atoms
- atoms with more than one electron
Electron correlation problem – difficulty when dealing with the repulsions between the electrons
- electron pathways are unknown, electron repulsions cannot be calculated exactly
To solve problem have to treat each electron as if it were moving in a field of charge that is the net result of
the nuclear attraction and the average repulsions of all the other electrons
-electrons are shielded from the nuclear charge by the repulsions of the other electrons
-have hydrogenlike orbitals – different sizes and energies
-when electrons are placed in a quantum level they prefer orbitals in the order of s, p, d, f
7.10 History of the Periodic Table
- Originally constructed to represent the patterns observed in the chemical properties of elements
Dobereiner (1780 – 1849) – found several groups of three elements that have similar properties
Newlands – 1864 suggested elements should be arranged in octaves
Myer and Mendeleev – constructed present form of table, found patterns and filled in gaps
- Difference between Mendeleev’s table and the current table is now elements are listed by atomic number
rather than atomic mass
7.11 The Aufbau Principle and the Periodic Table
- as protons are added one by one to the nucleus to build up the elements, electrons are similarly
added to these hydrogenlike orbitals
- 2 electrons per a orbitals with opposite spins
- mutually repulsive electrons occupy separate orbitals (ex. In 2p orbital)
Hund’s rule – the lowest energy configuration for an atom is the one having the max number of unpaired
electrons allowed by the Pauli principle in a particular set of degenerate orbitals
Valence electrons – electrons in the outermost principal quantum level of an atom
Core electrons – inner electrons
- Elements in the same group have the same valence electron configuration
Orbital filling points:
- the (n+1)s orbitals are always filled before the nd orbitals
- After lanthanum, fill the 4f orbital
- After actinium, fill the 5f orbital
-
The group labels of 1A, 2A, 3A, 4A, 5A, 7A, 8A indicate the total number of valence
electrons for the atoms in this group
- The above mentioned groups are called main-group, or representative elements
7.12 Periodic Trends in Atomic Properties
Ionization Energy – energy required to remove an electron from a gaseous atom or ion
First ionization energy – energy required to remove highest energy electron from an atom
Large jump in ionization energy when going from removing valence electrons to core electrons
-as go across a period from left to right, the first ionization energy increases
-as go down a group, first ionization energy decreases
Electron affinity – energy change associated with the addition of an electron to a gaseous atom
The more negative the energy, the great the quantity of energy being released
-generally becomes more negative across a period
-generally becomes more positive going down a group
Atomic radius – the distance between nuclei of atoms in compounds
-decrease going across a period (left to right)
-increase down a group
7.13 Properties of a Group: The Alkali Metals
Review of info found in Periodic Table
- Groups have similar chemical properties that change in a regular way. Number/type of
valence electrons determine an atom’s chemistry
The electron configuration
- Some groups have special names (ex. Alkali metals)
- Divided into metals and nonmetals.
Metals – give up one or more electrons to form positive ion, low ionization energy, left
side of table
Nonmetals – gain one or more electrons to form an anion, large ionization energy, most
negative electron affinity, right side of table
Metalloids (semi-metals) on division line. Have both metallic and nonmetallic properties
The Alkali Metals – Group 1A
Most chemically reactive of all metals
Agrees with general trends of first ionization energy and atomic radius
Smooth decrease in melting point and boiling point going down group
Lose valence electrons easily
Highly reactive with water
Multiple choice questions
1. Which of the following statements is true regarding sodium and chlorine?
A. Sodium has a greater electronegativity and larger first ionization energy
B. Sodium has a larger first ionization energy and larger atomic radius
C. Chlorine has a larger atomic radius and great electronegativity
D. Chlorine has great electronegativity and larger first ionization energy
E. Chlorine has a larger atomic radius and larger first ionization energy
2. Which of the following could be the quantum numbers for the valence electron in a potassium atom in its
ground state?
A. 3,0,0,1/2
B. 3,1,1,1/2
C. 4,0,0,1/2
D. 4,1,1,1/2
E. 4,2,1,1/2
3. Which of the following rules states that no two electrons in an atom can have the same set of quantum
numbers?
A. Hund’s rule
B. The Heisenberg uncertainty principle
C. The Pauli exclusion principle
D. The de Broglie hypothesis
E. The Bohr Model
4. Which of the following ions has the smallest ionic radius?
A. O^-2
B. F^-1
C. Na^+1
D. Mg^+2
E. Al^+3
5. Which of the following is an impossible set of quantum numbers?
A. 4,0,0,1/2
B. 4,0,1,1/2
C. 4,1,0,1/2
D. 4,1,1,1/2
E. 4,2,1,1/2
Free Response Question
1. a. Calculate the energy associated with an electron dropping from the excited n=6 state to ground state in
a hydrogen atom.
b. Calculate the wavelength of the emitted photon released during this process.
Answers
Multiple choice questions
1. D. As we move left to right in the periodic table, protons are added and the pull of the nucleus on the
electrons is increased. Thus, chlorine has a higher first ionization energy, greater electronegativity and a
smaller atomic radius.
2. C. Potassium’s valence electron is in the 4s orbital. Thus, n=4, l=0, ml=0, and ms=1/2 or -1/2.
3. C. The Pauli exclusion principle states that no two electrons in an atom can have the same set of
quantum numbers.
4. E. If you look at the periodic table you will find that all of the ions listed have the same electron
configuration as neutral neon. But because Al^+3 has the most protons (strongest attractive force) it has
the smallest ions.
5. B. The ml quantum number is a value between l and –l. Thus, it cannot be larger than the l quantum
number. So, 4,0,1,1/2 cannot exist because 1 is greater than 0.
Free response question
1a. Use equation E = -2.178·10^-18 J(Z^2/n^2)
For n=6
E = -2.178·10^-18 J(1^2/6^2) = -6.050 ·10^-20 J
For n=1
E= -2.178·10^-18 J(1^2/1^2) = -2.178·10^-18 J
▲E = energy of final state – energy of initial state
= -2.178·10^-18 J – (-6.050 ·10^-20 J) =
-2.117·10^-18 J
b. wavelength = hc/▲E
= (6.626 · 10^-34 J·s)(2.9979·10^8 m/s) / (2.117·10^-18 J) =
9.383·10^-8 m