Elementary physics

Elementary physics

Highly recommend:

Thinking Physics Is Gedanken Physics by Lewis Carroll Epstein

Understanding physics by Isaac Asimov

Physics is all calculus. Trying to do physics without calculus is like trying to run a race on one leg.

If the position of an object as a function of time is given by

$position=p(t)$

then the velocity is given by

$v={\frac {dp}{dt}}$

and the acceleration is given by

$a={\frac {dv}{dt}}={\frac {d^{2}p}{dt^{2}}}$

Velocity has units of distance per time (like miles per hour). Acceleration has units of distance per time per time.

The momentum of an object is equal to the mass times the velocity

$Momentum=mv$

The kinetic energy of an object is equal to half the mass times the velocity squared

$E={\frac {mv^{2}}{2}}$

In the image below a red object of unit mass moving with velocity 2 strikes a blue stationary object with equal mass. The total horizontal momentum, total vertical momentum, and total energy are unchanged by the collision. In other words, energy and momentum are Template:Link.

Before collision: Red object Horizontal momentum: 2 Vertical momentum: 0 Kinetic energy: 2 Blue object Horizontal momentum: 0 Vertical momentum: 0 Kinetic energy: 0 Total Horizontal momentum: 2+0 Vertical momentum: 0+0 Kinetic energy: 2+0

After collision: Red object Horizontal momentum: 1 Vertical momentum: 1 Kinetic energy: 1 Blue object Horizontal momentum: 1 Vertical momentum: -1 Kinetic energy: 1 Total Horizontal momentum: 1+1 Vertical momentum: 1+(-1) Kinetic energy: 1+1

A force of 1 Newton acting continuously on a mass of 1 kg will cause that mass to accelerate at 1 m/s²

$F=ma$

After the object has moved a distance of 2 meters it will have gained a kinetic energy of

$E=F\cdot distance=1\,Newton\cdot 2\,meters=2\,Joules$

Gravity on Earth causes all free falling objects to accelerate downward at 9.8 m/s²

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Atoms

External link: Periodic table at ptable.com

A red circle is an unpaired electron in the outermost shell.
A blue circle is a Template:Link of electrons.
Each electron shell is twice the radius of the previous shell.

File:Hydrogen shells.svg

File:Helium shells.svg

File:Lithium shells.svg	File:Beryllium shells.svg	File:Boron shells.svg	File:Carbon shells.svg
File:Nitrogen shells.svg	File:Oxygen shells.svg	File:Fluorine shells.svg	File:Neon shells.svg

File:Sodium shells.svg	File:Magnesium shells.svg	File:Aluminium shells.svg	File:Silicon shells.svg
File:Phosphorus shells.svg	File:Sulfur shells.svg	File:Chlorine shells.svg	File:Argon shells.svg

The next block of elements is more complex

A yellow circle is an unpaired electron in an inner shell. File:Potasium shells.svg The unpaired electron in Potassium is a conduction electron. Conduction electrons are Template:Link. File:Calcium shells.svg File:Scandium shells.svg File:Titanium shells.svg File:Vanadium shells.svg File:Chromium shells.svg File:Manganese shells.svg File:Iron shells.svg File:Cobalt shells.svg File:Nickel shells.svg File:Copper shells.svg File:Zinc shells.svg File:Gallium shells.svg File:Germanium shells.svg File:Arsenic shells.svg File:Selenium shells.svg File:Bromine shells.svg File:Krypton shells.svg Copper is whats known as a Template:Link. Zinc has a very low boiling point.

And the next block of elements is like it

A yellow circle is an unpaired electron in an inner shell. File:Rubidium shells.svg The unpaired electron in Rubidium is a conduction electron. Conduction electrons are Template:Link. File:Strontium shells.svg File:Yttrium shells.svg File:Zirconium shells.svg File:Niobium shells.svg File:Molybdenum shells.svg File:Technetium shells.svg File:Ruthenium shells.svg File:Rhodium shells.svg File:Palladium shells.svg File:Silver shells.svg File:Cadmium shells.svg File:Indium shells.svg File:Tin shells.svg File:Antimony shells.svg File:Tellurium shells.svg File:Iodine shells.svg File:Xenon shells.svg Silver is whats known as a Template:Link. Cadmium has a very low boiling point.

And the next block of elements is even more complex

A blue-green circle is an electron pair in an f-block subshell. File:Caesium shells.svg The unpaired electron in Caesium is a conduction electron. Conduction electrons are Template:Link. File:Barium shells.svg File:Lanthanum shells.svg File:Cerium shells.svg File:Praseodymium shells.svg File:Neodymium shells.svg File:Promethium shells.svg File:Samarium shells.svg File:Europium shells.svg File:Gadolinium shells.svg File:Terbium shells.svg File:Dysprosium shells.svg File:Holmium shells.svg File:Erbium shells.svg File:Thulium shells.svg File:Ytterbium shells.svg File:Lutetium shells.svg File:Hafnium shells.svg File:Tantalum shells.svg File:Tungsten shells.svg File:Rhenium shells.svg File:Osmium shells.svg File:Iridium shells.svg File:Platinum shells.svg File:Gold shells.svg File:Mercury shells.svg File:Thallium shells.svg File:Lead shells.svg File:Bismuth shells.svg File:Polonium shells.svg File:Astatine shells.svg File:Radon shells.svg Gold is whats known as a Template:Link. Mercury has a very low boiling point.

And the next block of elements is like it.

A blue-green circle is an electron pair in an f-block subshell. File:Francium shells.svg The unpaired electron in Francium is a conduction electron. Conduction electrons are Template:Link. File:Radium shells.svg File:Actinium shells.svg File:Thorium shells.svg File:Protactinium shells.svg File:Uranium shells.svg File:Neptunium shells.svg File:Plutonium shells.svg File:Americium shells.svg File:Curium shells.svg File:Berkelium shells.svg File:Californium shells.svg File:Einsteinium shells.svg File:Fermium shells.svg File:Mendelevium shells.svg File:Nobelium shells.svg File:Lawrencium shells.svg File:Rutherfordium shells.svg File:Dubnium shells.svg File:Seaborgium shells.svg File:Bohrium shells.svg File:Hassium shells.svg File:Meitnerium shells.svg File:Darmstadtium shells.svg File:Roentgenium shells.svg File:Copernicium shells.svg File:Nihonium shells.svg File:Flerovium shells.svg File:Moscovium shells.svg File:Livermorium shells.svg File:Tennessine shells.svg File:Oganesson shells.svg

Note: The metallic forms of the elements have electronic structures that differ slightly from the one the Template:Link predicts.

Each unpaired electron in the outermost shell (called the valence shell) forms a Template:Link with an unpaired electron in the outermost shell of a neighboring atom.

Pure Template:Link gas consists of Template:Link.

File:H2 shells.svg

Template:Link (H₂), Template:Link (F₂), Template:Link (Cl₂), Template:Link (Br₂), and Template:Link (I₂) all form Template:Link.
So does Template:Link (N₂) and Template:Link (O₂).

Atoms that have no unpaired electrons in their valence shell are called Template:Link. Noble gases do not form chemical bonds and are therefore Template:Link.
Template:Link (He), Template:Link (Ne), Template:Link (Ar), Template:Link (Kr), Template:Link (Xe), and Template:Link (Rn) are noble gases.

File:Helium shells.svg

File:Neon shells.svg

File:Argon shells.svg

File:Krypton shells.svg

File:Xenon shells.svg

File:Radon shells.svg

A single molecule of Template:Link consists of one Fluorine atom and one hydrogen atom and is therefore diatomic.
Fluorine is a powerful Template:Link. In fact, Fluorine is the most Template:Link element known. (It really likes electrons).
Fluorine is much more electronegative than hydrogen. This causes Hydrogen Fluoride to be a Template:Link.

File:HF shells.svg

A single molecule of Template:Link (H₂O) consists of one oxygen atom and two hydrogen atoms.
Water is a polar molecule.

File:H2O shells.svg

A single molecule of Template:Link (NH₃) consists of one nitrogen atom and three hydrogen atoms.
Ammonia is a polar molecule.

File:NH3 shells.svg

A single molecule of Template:Link (CH₄) consists of one carbon atom and four hydrogen atoms.
Methane is a hydrocarbon. Hydrocarbons are non-polar molecules and therefore not soluble in water.
Methane is a gas. It boils at -161 °C.

File:Methane shells.svg

A single molecule of Template:Link (C₂H₆) consists of two carbon atoms and six hydrogen atoms.
Ethane is a gas. It boils at -88 °C.

File:Ethane shells.svg

A single molecule of Template:Link (C₂H₆O), also known as drinking alcohol, consists of two carbon atoms, six hydrogen atoms, and one oxygen atom.
Template:Link.

File:C2H6O shells.svg

A single molecule of Template:Link (C₈H₁₈) consists of eight carbon atoms and eighteen hydrogen atoms.
Octane is a liquid. It boils at 125 °C.
If the chain were even longer and the hydrogen atoms were replaced with fluorine atoms then you would have Template:Link.

File:C8H18 shells.svg

But Benzene is a little bit different.
A single molecule of Template:Link consists of six carbon atoms and six hydrogen atoms arranged in a ring. Each carbon atom bonds with 2 other carbon atoms and with one hydrogen atom thus accounting for three unpaired electrons per carbon atom. But, as we already know, each carbon atom has four unpaired electrons so one electron per carbon atom is unaccounted for. There are six carbon atoms therefore a total of six electrons per benzene molecule are unaccounted for. Those six Template:Link form the blue circle around the molecule. See also: Template:Link, Template:Link, and Template:Link. Benzene molecules are shaped like flat plates. (See Template:Link.)

File:C6H6 shells.svg

A single molecule of Template:Link consists of five carbon atoms, five hydrogen atoms, and one nitrogen atom arranged in a ring. Six unpaired electrons form the blue ring around the molecule.
Pyridine is a nitrogen Template:Link.

File:C5H5N shells.svg

Template:Link consists of carbon atoms densely packed in a regular hexagonal pattern:

File:Graphen.jpg

Template:Link consist of a two-dimensional hexagonal lattice of carbon atoms, bent and joined in one direction so as to form a hollow cylinder:

File:Carbon nanotube zigzag povray cropped.PNG

A single molecule of Template:Link is a Template:Link of carbon atoms:

File:Buckminsterfullerene animated.gif

Template:Link is a Template:Link:

File:BF3 shells.svg

Its Boron atom has a vacant orbital which can form a covalent bond by sharing a lone pair of electrons on an atom in a base (in this case ammonia):

File:BF3 reacting with ammonia.svg

A molecule of Template:Link consists of one Antimony atom and five Fluorine atoms.

File:SbF5 shells.svg

Its Antimony atom has a vacant orbital which can form a covalent bond by sharing a lone pair of electrons with a sixth Fluorine atom (actually its an ion) thus creating Antimony hexafluoride.

File:SbF6 shells.svg

Note that the molecule in the image above has a net negative charge of -1.

I would guess that the reason the six pairs of electrons are able to share the outer electron shell in antimony is because of sd⁵ Template:Link.

Antimony hexafluoride Template:Link form a Template:Link with Template:Link ions creating Template:Link which is the strongest Template:Link known with Template:Link=-28.

Thats 10¹⁶ times stronger than 100% Template:Link which has H₀=-12.

It has been shown to Template:Link even hydrocarbons (which cannot normally be "protonated"). It can only be stored in containers lined with Teflon.

File:Proton Zundel.gif

Protons tunnel across a series of hydrogen bonds between Template:Link and water molecules.

From Wikipedia:Grotthuss mechanism:

Proton jumping is the process by which an 'excess' proton diffuses through the Template:Link network of water molecules or other hydrogen-bonded liquids through the formation and concomitant cleavage of covalent bonds involving neighboring molecules. The details of the hopping and transport mechanism are still debated.

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References

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