Intermediate chemistry


 * See also: and Spatial_structure_of_the_electron



The first pair of electrons fall into the ground shell. Once that shell is filled no more electrons can go into it. Any additional electrons go into higher shells.

The nucleus however works differently. The first few neutrons form the first shell. But any additional neutrons continue to fall into that same shell which continues to expand until there are 49 pairs of neutrons in that shell.


 * The highest energy gamma rays emitted by nuclei are around 10 Mev which corresponds to a wavelength of 124 fm.

The electric force between two electrons is times stronger than the gravitational force. (12,242 * 2128)

The energy required to assemble a sphere of uniform charge density = $$\frac{3}{5}\frac{Q^2}{4 \pi \epsilon_0 r}$$


 * For Q=1 electron charge and r=1.8506 angstrom thats . That energy is stored in the electric field of the electron.


 * The energy per volume stored in an electric field is proportional to the square of the field strength so twice the charge has 4 times as much energy.


 * 4*4.669 = 18.676.

Mass of electron = Me = 510,999 ev

Mass of proton = Mp = 938,272,000 ev

Mass of neutron = Mn = 939,565,000 ev


 * Mn = Mp + Me + 782,300 ev

Mass of muon = Mμ = 105.658 ev = 206.7683 * Me

Mass of helium atom = 3,728,400,000 = 4*Me+4*Mp -52.31 Me


 * The missing 52.31 electron masses of energy is called the mass deficit or nuclear binding energy. Fusing hydrogen into helium releases this energy.

Iron can be fused into heavier elements too but doing so consumes energy rather than releases energy.



The total outward force for a solid 4-dimensional sphere of uniform density in Clifford rotation is $$\frac{4}{5} \cdot \frac{m v^2}{r}$$

The angular momentum of a solid 4-dimensional sphere of uniform density is $$\frac{2}{3} \cdot mvr$$

Empirically determined values for the size of atoms:


 * Diatomic Hydrogen (Z=2) = 1.9002 angstroms


 * Helium (Z=2) = 1.8506 angstroms

In 3 dimensions the force between 2 electrons is:


 * $$F = \frac{1}{4\pi\varepsilon_0} { e_1 e_2 \over r^2}$$


 * where me is the electron's mass, e1 is the charge of the electron,


 * $$\varepsilon_0 = \frac{1}{180.95} \frac{e^2}{\text{eV} Å}$$


 * but in 4 dimensions:


 * $$\varepsilon = \frac{2 \varepsilon_0}{\pi r} $$


 * where r is the distance at which the inverse square law gives the same result as the inverse cube law. In other words, the distance at which the inverse square law of the macroscopic world gives way to the inverse cube law of the microscopic world.

The angular momentum is:
 * $$ \frac{2}{3} \cdot m_\mathrm{e} v r = \hbar $$


 * where ħ is reduced Planck constant


 * $$\hbar={{h}\over{2\pi}} = 1.054\ 571\ 800(13)\times 10^{-34}\text{J}{\cdot}\text{s}$$


 * Therefore:


 * $$v = \frac{3}{2} \cdot \frac{\hbar}{m_\mathrm{e}} \frac{1}{r}$$

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Density and thermal expansion
Densities:


 * Crystalline solids: 1.2
 * Amorphous solids: 1.1
 * liquids: 1

Water ice is an exception. Ice has a density of 0.9167

From Thermal expansion

Thermal expansion generally decreases with increasing bond energy, which also has an effect on the melting point of solids, so, high melting point materials are more likely to have lower thermal expansion. In general, liquids expand slightly more than solids. The thermal expansion of glasses is higher compared to that of crystals.

For an ideal gas, the volumetric thermal expansion (i.e., relative change in volume due to temperature change) depends on the type of process in which temperature is changed. Two simple cases are where the pressure is held constant (Isobaric process), or when the volume (Isochoric process) is held constant.

The derivative of the ideal gas law, $$PV = T $$, is


 * $$P dV + V dP = dT$$

where $$P$$ is the pressure, $$V$$ is the specific volume, and $$T$$ is temperature measured in energy units.

By definition of an isobaric thermal expansion, we have $$dP=0$$, so that $$P dV=dT$$, and the isobaric thermal expansion coefficient is


 * $$\alpha_{P = C^{te}} \equiv \frac{1}{V} \left(\frac{d V}{d T}\right) = \frac{1}{V} \left(\frac{1}{P}\right) = \frac{1}{PV} = \frac{1}{T}$$.

Similarly, if the volume is held constant, that is if $$dV=0$$, we have $$V dP=dT$$, so that the isovolumic thermal expansion is


 * $$\alpha_{V=C^{te}} \equiv \frac{1}{P} \left(\frac{d P}{d T}\right) = \frac{1}{P} \left(\frac{1}{V}\right) = \frac{1}{P V} = \frac{1}{T}$$.

For a solid, we can ignore the effects of pressure on the material, and the volumetric thermal expansion coefficient can be written:



\alpha_V = \frac{1}{V}\,\frac{dV}{dT} $$

where $$V$$ is the volume of the material, and $$dV/dT$$ is the rate of change of that volume with temperature.

This means that the volume of a material changes by some fixed fractional amount. For example, a steel block with a volume of 1 cubic meter might expand to 1.002 cubic meters when the temperature is raised by 50 K. This is an expansion of 0.2%. If we had a block of steel with a volume of 2 cubic meters, then under the same conditions, it would expand to 2.004 cubic meters, again an expansion of 0.2%. The volumetric expansion coefficient would be 0.2% for 50 K, or 0.004% K−1.

If we already know the expansion coefficient, then we can calculate the change in volume



\frac{\Delta V}{V} = \alpha_V\Delta T $$

where $$\Delta V/V$$ is the fractional change in volume (e.g., 0.002) and $$\Delta T$$ is the change in temperature (50 °C).

For common materials like many metals and compounds, the thermal expansion coefficient is inversely proportional to the melting point. In particular for metals the relation is:

\alpha \approx \frac{0.020}{M_P} $$ for halides and oxides

\alpha \approx \frac{0.038}{M_P} - 7.0 \cdot 10^{-6} \, \mathrm{K}^{-1} $$

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Quasiparticles

 * See also: List of quasiparticles and Quasiparticle

A hole is a region with a net surplus of positive charges. An anti-hole is a region with a net surplus of negative charges. Electricity is the flow of holes and anti-holes.

A flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of either positive or negative charges, or both, a convention is needed for the direction of current that is independent of the type of charge carriers. The direction of conventional current is arbitrarily defined as the same direction as positive charges flow.



A p-type semiconductor only conducts holes. An n-type semiconductor only conducts anti-holes. Holes and anti-holes combine at the junction of a forward biased diode.
 * In the case of a light emitting diode the combining of electrons and holes results in the creation of light.

Electricity will not flow through a reverse biased diode because this would require holes and anti-holes to form at and move in opposite directions away from the junction.
 * However, in the case of a photodiode, current can be induced to flow by shining a light on the junction.



A transistor can be thought of as two diodes placed end-to-end (i.e. in series). When there is a voltage drop between the collector and the emitter then one diode is forward biased and the other diode is reverse biased. Because one of the diodes is reverse biased current will not flow. However current will flow from the collector to the emitter when a small amount of current is allowed to pass through the base.

To understand why this happens it helps to imagine that the forward biased diode is a light emitting diode and the reverse biased diode is a photodiode. (Such a transistor is called a photon coupled transistor.) When current is allowed to pass through the base light is created by the light emitting diode. This light is then absorbed by the photodiode and therefore current is able to pass from collector to emitter. This in turn creates still more light which allows still more current to pass. If the photodiode absorbed 100% of the light emitted than the current would flow forever. Since not all the light created by the light emitting diode is absorbed by the photodiode the current will decay rapidly.

The total amount of current that flows from collector to emitter will be some multiple of the current that originally flowed through the base.

From Exciton:

An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and in some liquids. The wavefunction of the bound state is said to be hydrogenic, an exotic atom state akin to that of a hydrogen atom. However, the binding energy is much smaller and the particle's size much larger than a hydrogen atom. This is because of both the screening of the Coulomb force by other electrons in the semiconductor (i.e., its dielectric constant), and the small effective masses of the excited electron and hole. Provided the interaction is attractive, an exciton can bind with other excitons to form a biexciton, analogous to a dihydrogen molecule.