Structure of Matter

Important Discoveries About the AtomLaw of Conservation of Matter

◦ In 1774, Antoine Lavoisier performed experiments & measurements that led to this law.

◦ In chemical reactions, matter cannot be created nor destroyed

Law of Constant Composition◦ In 1700, Joseph Proust mad measurements on

chemical reactions and compounds to develop this law

◦ Each pure chemical compound always has the same percentage composition of each element by mass.

These laws led John Dalton to develop his theory.

Important Discoveries About the AtomDalton’s Atomic Theory states that:

◦All matter is composed to tiny, indivisible particles, called atoms, that cannot be created or destroyed.

◦Each element has atoms that are identical to each other in all of their properties, and these properties are different from the properties of all other atoms.

◦Chemical reactions are simple rearrangements of atoms from one combination to another in small whole-number ratios.

Important Discoveries About the AtomDalton’s atomic theory led him to

propose the …◦Law of Multiple Proportions

When 2 elements can be combined to made 2 different compounds, and if samples of these 2 compounds are taken so that the masses of one of the elements in the 2 compounds are the same in both samples, then the ratio of the masses of the other element in these compounds will be a ratio of small whole numbers.

Law of Multiple Proportions

Important Discoveries About the AtomIn 1834, Michael Faraday showed

that an electric current could cause chemical reactions to occur, demonstrating the electric nature of the elements.

In the 1870s the cathode ray tube was developed by Sir William Crookes. ◦He mistakenly thought that the

cathode rays were negatively charge molecules instead of electrons.

Important Discoveries About the AtomIn 1897, J.J. Thomson determined

that cathode rays were a fundamental part of matter he called electrons.

Thomson also discovered the electron’s charge to mass ratio, (e/m = -1.76 × 108 coulombs per gram) by measuring the deflection of the cathode rays in the presence of electric and magnetic fields.

J.J. Thomson

Important Discoveries About the AtomOil Drop Experiment

◦In 1909, Robert Millikan performed this experiment. He determine the charge of an electron to be -1.60 × 10-19 coulomb.

◦Using Thomson’s charge to mass ratio, he then calculated the mass of an electron= 9.11 × 10-28g.

Important Discoveries About the AtomFrom those experiments, the

plum pudding model was developed, which has electrons swimming in a sea of positive charges.

Important Discoveries About the AtomGold Foil Experiment

◦Performed by Ernest Rutherford in 1910. He was interested in radioactive

materials, alpha & beta particles had already been discovered. Rutherford’s Nuclear

Model

Important Discoveries About the AtomIn 1919, Rutherford also

discovered the proton with a mass of 1.67×10-24g.◦ It’s 1836 times bigger than an

electronHis student, James Chadwick,

discovered the nucleus in 1932. It has almost the same mass as a proton.

Subatomic ParticlesName Symbo

lAbsolute charge (coulombs)

Absolute mass (g)

Relative charge

Relative mass

Electron e or e- -1.602×10-

19

9.109×10-28

-1 5.486×10-4

Proton p or p+

+1.602×10-19

1.673×10-24

+1 1.0073

Neutron n or n0 0 1.675×10-24

0 1.0087

Important Discoveries About the AtomWhile all of this stuff was happening,

other physicists were interested in the interaction between light and matter. (mid-1800s)◦One thing they discovered was that each

element, when heated or sparked with electricity, gives off characteristic colors. A spectroscope was used to show these

colors consist of discrete wavelengths of light (line spectra), not the uniform rainbow. The line spectra for most elements & compounds can

be complex but hydrogen’s is relatively simple.

Important Discoveries About the Atom

Important Discoveries About the AtomIn 1885, Johann Balmer found a

mathematical relationship between the wavelengths of the lines in the visible light region of the spectrum.◦Similar lines were discovered in the

infrared (Paschen series) and ultraviolet (Lyman series) regions.

◦Johannes Rydberg extended Balmer’s equations so that all of the wavelengths could be predicted.

Important Discoveries About the AtomPlanetary or Solar System Model

◦Proposed by Niels Bohr in 1913. He assumed that electrons move around the nucleus in only certain circular orbits.

◦Max Planck described light as packets or quanta of energy called photons.

Important Discoveries About the Atom In 1924, Louis de Broglie suggested that if light can

be considered as particles, then the small particles (electrons) may also have the characteristics of waves!

In 1927, Erwin Schrödinger applied mathematical equations for waves to electrons in the atom and began the wave-mechanical model of the atom.◦ For the hydrogen atom, the results are very similar to

Bohr’s model of the atom except the electron doesn’t follow a precise orbit. The position of the electron is described as a probable location.

◦ Werner Heisenberg developed the uncertainty principle in the 1920s that says the position & momentum of any particle cannot be both known exactly at the same time. As you know one more precisely, the other becomes less certain.

Atomic StructureAn atom usually exists in the lowest

possible energy state – called the ground state.

An atom that has more energy than the ground state is said to be in an excited state.

When at atom loses energy in going from an excited state to the ground state, that energy is emitted as light.

Atomic Structure

Atomic StructureWavelength, Frequency, & Energy

of Light◦All EM radiation may be considered

as waves defined by wavelength (λ) & frequency (ν). Wavelength – distance between 2

repeating points on a sine wave. Frequency – the # of waves that pass a

point in space each second

Atomic StructureWavelength and frequency are

inversely proportional to each other.

(wavelength)(frequency) = speed of light

λν = c

c = 3.00×108m/sλ= metersν = s-1 or 1/s

Atomic StructureMax Planck discovered that the

energy of the EM waves is proportional to the frequency & inversely proportional to the wavelength

hν = E Planck’s constant (h)

h = E h = 6.63×10-34Js λ

Atomic StructureThe Bohr Model- requires the

electrons in the atom be confined to specific, allowed orbits. Using physics, the energy of an orbit with the number, n, is

En = -2πme4 = -2.178×10-18joule

n2h2 n2

Where m = mass e-, e = charge on e-, h = Planck’s constant, & n = principal quantum number

n also represents the number of each orbit in Bohr’s model, starting with the one closet to the nucleus

Atomic StructureBohr’s orbitsEnergy, in the form of light, is emitted

from an atom when an electron moves from an orbit to a lower-numbered orbit.

When an electron is promoted to a higher numbered orbit, energy must be added.

The energy difference between 2 orbits is constant so you know how much energy is being released when the electron drops down to its original orbit. You use the equation in the last slide to calculate the energy difference.

Atomic StructureEmitting light

Another representation

Hydrogen

Atomic StructureBohr also thought that the momentum

(mass × velocity) of the electron be related to the size of the electron’s orbit.

Mv = nh 2πrFor hydrogen (n = 1), the radius of the

electron was calculated to be 53pm, called the Bohr radius. The radii of other orbits are all whole-number multiples of it.◦ Gave chemists a theoretical value for the size of

a hydrogen atom.Bohr won a Noble Prize for all this. Go Bohr!

Atomic StructureWave-Mechanical Model of the Atom

◦After Bohr’s achievement, Louis deBroglie ascertained that electrons could also act as waves, not just particles. 1 way of looking at this duality, is to look at the

equation for the energy of a wave… E = hv = h = mc2

λ Rearranging this equation, you can see the

relationship between the mass of the electron and the wave (frequency) … = h = mc2

λ

Atomic StructureDescribing the motion of an electron, however,

requires complex “wave equations” and higher level calculus (differential equations) than is taught in high school. But understanding the results of these wave equations can be done:◦ Wave equations require 3 numbers, called quantum

numbers, in order to reach a solution. The principal quantum number, n The azimuthal quantum number, l The magnetic quantum number, ml

And a 4th, unique, quantum number, the spin quantum number, ms

There are specific rules for applying these numbers to electrons but it isn’t required on the AP test.

Atomic Structure◦The wave equations changed the

picture of the atom completely. The fixed orbits of the Bohr model are replaced with a cloud of electrons around the nucleus. The modern orbital is the region of space in which there is the greatest (90%) probability of finding an electron.Bohr orbit as fixed

ringsProbability plot of electrons in the 1st orbit

Probability plot with 90% of electrons within circle

Atomic Structure◦The circular orbits of the Bohr theory are

replaced with spherical electron clouds. The wave equations have shown that most electron clouds have shapes that are more complex than Bohr’s orbits but are still simple geometric shapes.

◦The arrangement of electrons deduced from the wave equations agrees well with the periodic table. Many physical & chemical properties of elements & compounds are more fully understood with knowledge gained about the electronic structure & orbital shape.

Atomic Structure◦The results of the wave equations

agree completely with the Bohr model. Specifically, the energy change for an electron moving from one electron cloud to another. Also the 53pm radius found for the electron in the hydrogen atom still holds true.

◦The Heisenberg uncertainty principle is fundamental to the wave mechanical model. The exact location and momentum of an electron cannot be known at the same time.

Atomic StructurePrincipal energy levels (shells)

◦Another term for principal quantum number

◦There are a maximum of 7 shells in an atom.

◦1st shell is closest to the nucleus, the 7th is farthest away.

◦As they become larger, the further away from the nucleus, the more electrons they can hold.

Atomic StructureSublevels (subshells)

◦Each principal energy level contains one or more sublevels, or the azimuthal quantum number, l. l can never be greater than n-1.

◦How many sublevels can each principal energy level hold? The same number as the value of n for that

energy level. Ex. n = 3? It has 3 sublevels. n = 6? It has 6 sublevels. However, for the 118 known elements, only 4 of the sublevels are used.

SublevelsPrincipal level, n Sublevel number,

lSublevel letter

1 0 s

2 0, 1 s, p

3 0, 1, 2 s, p, d

4 0, 1, 2, 3 s, p, d, f

5* 0, 1, 2, 3 s, p, d, f

6* 0, 1 ,2 s, p ,d

7* 0, 1 s, p*Only sublevels used by known elements are shown here.

Atomic StructureOrbitals

◦Each sublevel may contain one or more electron orbitals, a region of space that has a high electron density. Each orbital may hold a maximum of 2

electrons. In order to share the orbital, the electrons must

have opposite spins. The number of orbitals a sublevel can have

depends on its azimuthal quantum number, l, and is equal to 2l +1.

OrbitalsSublevel number, l

Sublevel letter

Number of orbitals 2l + 1

Number of electrons per Sublevel

0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14

Each orbital is given a magnetic quantum number, ml. Values range from –l to +l.

orbital ml. values

s 0

p -1, 0, +1

d -2, -1, 0, +1, +2

f -3, -2, -1, 0, +1, +2, +3

Orbital shapes

Electronic Structure of the Atom

                                                                                                                                                                                                                         

  s   p  d   f

7s 7p

6s 6p 6d

5s 5p 5d 5f

4s 4p 4d 4f

3s 3p 3d

2s 2p

1s

start

Orbital filling diagram

Electron ConfigurationsSome rules to abide by:

◦Aufbau Principle – electrons fill the lowest available energy level before moving to a higher one.

◦Some exceptions:

Element Electron Configuration

Copper, Cu 1s22s22p63s23p64s13d10

Silver, Ag 1s22s22p63s23p64s23d104p65s14d10

Gold, Au 1s22s22p63s23p64s23d104p65s24d105p66s14f145d10

Chromium, Cr

1s22s22p63s23p64s13d5

Molybdenum. Mo

1s22s22p63s23p64s23d104p65s14d5

Abbreviated Electron Configurations- Use noble gases

                                                                                                                                                                                                                         

  s   p  d   f

1234567

Example

Fe = 1s22s22p63s23p64s23d6

Fe = [Ar]4s23d6

Valence ElectronsMany times, chemists are only

interested in the outermost electrons in an atom, the valence electrons.◦Only s and p electrons are valence

electrons.

Orbital DiagramsHund’s Rule

◦p, d, or f orbitals in a sublevel must all be filled with one electron each before a 2nd electron is allowed to pair in any orbital.

Quantum NumbersPrincipal quantum number, n = 1-7Azimuthal quantum number, l = n-1 = 0-6Magnetic quantum number ml = -l -0-+l Spin quantum number, ms = + ½ or – ½

Lowest possible values for each quantum number are used 1st.

Pauli exclusion principle- no 2 electrons can have the exact same quantum number

While writing the quantum numbers is not on the AP test, knowing what they look like according to the rules is.

See handout.

Quantum numbers, what do they mean?Principal quantum number, n – represents

the average distance of the electron from the nucleus, or the size of the principal energy level.

Azimuthal quantum number, l – represents the shape(s) of the orbitals within the sublevel.

Magnetic quantum number ml – represents the oreientation of each orbital in space on an x, y, z axis.

Spin quantum number, ms – represents the “spin” of the electrons.