Elements

Size of atoms
Dot size corresponds to atom size.

For gases, the density at boiling point is used.   Size data

Density

Copper atoms stack like cannonballs. We can calculate the atom size by assuming the atoms are shaped like either cubes or spheres. For copper atoms,

```Density         = D              = 8900 kg/m3
Mass            = M              = 9.785e-26 kg
Number density  = N   =  D / M   = 9.096e28 atoms/m3
Cube volume     = Υcube= 1 / N    = 1.099e-29 m3          Volume/atom if the atoms are cubes
Cube length     = L   =  Υ1/3cube = 2.22e-10 m            Side length of the cube
Sphere fraction = f   =  π/(3√2) = .7405                 Fraction of volume occupied by spheres in a stack o spheres
Sphere volume   = Υsph =  Υcube f = 8.138e-30 m3 = 4⁄3πR3  Volume/atom if the atoms are spheres
Sphere radius   = R              = 1.25e-10 m
```

Strength and melting point
```Dot size   = (Shear Modulus)1/3      A measure of a material's strength
Dot color  =  Melting point

White  =  Highest melting points
Red    =  Lowest melting points
Blue   =  Elements that are a gas or a liquid at room temperature and pressure.
Liquids and gases have a shear modulus of 0.
```
Rocket nozzles are made from materials with a high melting point, a high shear strength, and a high atomic mass. Tungsten is the element of choice, especially because it's vastly cheaper than Rhenium, Osmium, and Iridium.

For carbon, the values are given for diamond form.

Shear data Melt data

Strength and density
```Color     =  Shear Modulus
Dot size  =  Density
```
Shear data Density data
Strength to weight ratio

```Color      =  Shear Modulus / Density          A measure of a material's "strength to weight" ratio
Dot size   =  Density
```
The metals with the highest strength to weight ratio are Chromium, Ruthenium, and Beryllium.

Chromium is common in the Earth's crust and Ruthenium is rare.

Shear data Density data

High temperature materials
```          Density Melt  Boil  Young Young   \$/kg  ppm in metallic
g/cm^3   K     K     GPa  /rho          asteroid
Tungsten   19.25  3693  5828   411   21.4     50     ~ 1
Rhenium    21.0   3459  5869   463   22.0   4600     ~ 1
Osmium     22.59  3306  5285   550   24.3  12000       2
Tantalum   16.7   3290  5731   186   11.1    400     ~  .5
Molybdenum 10.28  2896  4912   329   31.0     21     ~10
Niobium     8.75  2750  5017   105   12.0     40     ~ 3
Iridium    22.4   2739  4701   528   23.6  14000       2
Ruthenium  12.45  2607  4423   447   35.9   5500       5
Hafnium    13.31  2506  4876    78    5.9    500     ~ 1
Rhodium    12.41  2237  3968   380   30.6  90000       2
Thorium    11.7   2115  5061    79    6.8            ~  .5
Platinum   21.45  2041  4098   168    7.8  55000       9
Vanadium    6.0   2183  3680   128   21.3              0
Chromium    7.19  2180  2944   279   38.8              0
Zirconium   6.52  2128  4682    88   14.5              0
Titanium    4.51  1941  3560   116   25.7              0
Palladium  12.02  1828  3236   121   10.1            ~ ?
Iron        7.87  1811  3134   211   26.8         100000
Nickel      8.91  1728  3186   200   22.4          10000
Cobalt      8.90  1768  3200   209   23.5         ~ 1000
Uranium    19.1   1405  4404   208   10.9              1
Beryllium   1.85  1560  2742   287  155.1              0
Manganese   7.21  1519  2334   198   27.5              0
Aluminum    2.70   933  2792    70   25.9              0
Magnesium   1.74   923  1363    45   25.9              0
```

Conductivity

```Red:   Lowest conductivities
White: Highest conductivities
```
If an element's conductivity is more than 2 orders of magnitude less than that of silver then it is left blank.

Resistivity data

History

Discovery
```        Earliest   Shear    Melt  Density
known use  Modulus  (K)   (g/cm^3)
(year)     (GPa)
Wood    < -10000     15        -    .9
Rock    < -10000
Carbon  < -10000      -
Diamond < -10000    534     3800   3.5
Gold    < -10000     27     1337  19.3
Silver  < -10000     30     1235  10.5
Sulfur  < -10000
Copper     -9000     48     1358   9.0
Brass      -5000    ~40                    Copper + Zinc
Bronze     -3000    ~40                    Copper + Tin
Tin        -3000     18      505   7.3
Antimony   -3000     20      904   6.7
Mercury    -2000      0      234  13.5
Iron       -1200     82     1811   7.9
Arsenic     1649      8     1090   5.7
Cobalt      1735     75     1768   8.9     First metal discovered since iron
Platinum    1735     61     2041  21.4
Zinc        1746     43      693   7.2
Tungsten    1783    161     3695  19.2
Chromium    1798    115     2180   7.2

Stone age    antiquity
Copper age    -9000
Bronze age    -3500
Iron age      -1200
```
Bronze holds an edge better than copper and it is more corrosion resistant.

Gold was the densest known element until the discovery of platinum in 1735. This made it impossible to counterfeit as a currency.

Metals known since antiquity
```Horizontal axis:  Density
Vertical axis:    Shear modulus / Density       (Strength-to-weight ratio)
```

Metals

```Horizontal axis:  Density
Vertical axis:    Shear modulus / Density       (Strength-to-weight ratio)
```
Metals with a strength-to-weight ratio less than lead are not included, except for mercury.
Abundance

Solar abundance

```Dot size =  log(SolarAbundance)
```
Elements with a dot size of zero have no stable isotope.

Solar abundance data

Price

```Color    =  Price per kilogram
Dot size = -log(SolarAbundance)      The smaller the dot, the more abundant the element.
```
Price data
Chemistry

Bohr model of the atom

The "de Broglie wavelength" of a particle is

```Particle momentum    =  Q
Planck constant      =  h  =  6.62*10^-34 Joule seconds
Particle wavelength  =  W  =  h/Q             (de Broglie formula)
```
The Bohr hypothesis states that for an electron orbiting a proton, the number of electron wavelengths is an integer. This sets the characteristic size of a hydrogen atom.
```Orbit circumference  =  C  =  N W           where N is a positive integer

N   Orbital

1     S
2     P
3     D
4     F

Electron mass      =  m                =  9.11*10-31 kg
Electron velocity  =  V
Electron momentum  =  Q  = m V
Electron charge    =  e                =  -1.60*10-19 Coulombs
Coulomb constant   =  K                =  9.0*109  Newtons meters / Coulombs2
Electric force     =  Fe  =  K e2 / R2
Centripetal force  =  Fc  =  M V2 / R
Orbit radius       =  R  =  N h2 / (4 π2 K e2 m)  =  N * 5.29e-11 meters
Electron energy    =  E  =  - .5 K e2 / (R N2)    =  N-2 2.18e-18 Joules  =  N-2 13.6 electron Volts          (Ionization energy)
```
For an electron on a circular orbit,
```Fe = Fc
```

Wavefunctions

Shells

Electronegativity

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