The Scottish Saltire and field is one of the key components of the Union Flag. The Union Flag has been used in a variety of forms since 1606, when the flags of the Kingdom of Scotland and Kingdom of England were first merged to symbolise the Union of the Crowns. (The Union of the Crowns having occurred in 1603.) In Scotland, and in particular on Scottish vessels at sea, historical evidence suggests that a separate design of Union Flag was sometimes flown to that used in England. Following the Acts of Union of 1707, which united the Kingdom of Scotland and the Kingdom of England, the standard Union Flag became the national flag of the new United Kingdom of Great Britain.
From 1801, in order to symbolise the union of the Kingdom of Great Britain with the Kingdom of Ireland, a new design was adopted for the Union Flag of the United Kingdom of Great Britain and Ireland. The 1801 design did not change with the partition of Ireland in 1921 and creation of the Irish Free State, and is the flag of the United Kingdom of Great Britain and Northern Ireland today.
The Royal Standard of the King of Scots, also known as the Royal Flag of Scotland or the Lion Rampant, is the flag used historically by the King of Scots. It remains the personal banner of the monarch and use of this flag is restricted under the Act of the Parliament of Scotland 1672 cap. 47 and 30 & 31 Vict. cap. 17.
Despite the legal restrictions concerning the use of this flag, it is often regarded as a second, albeit unofficial, national flag for Scotland, most often seen at sporting events.
Scanning tunneling microscope
Scanning tunneling microscopy (STM) is a way to view the shape of tiny objects. It can make pictures of atoms on a surface and move the atoms to different places. It was invented by Gerd Binnig and Heinrich Rohrer in 1981 at IBM, in Zürich. In 1986 they won the Nobel Prize in Physics for inventing it.
The STM is called a microscope because it makes pictures of tiny objects. But it is different -- it doesn't have anything to look into with our eyes. It is similar to feeling the shape of objects on a table in a dark room: you can draw a picture of the shape even though you did not seen it with your eyes. The STM does this for very tiny objects. It works by scanning a sharp metal needle back and forth across a surface, and uses electric current instead of force to sense the shape. When the tip of sharp metal needle is brought very close to the surface of a thing being studied, a voltage between the two causes electrons to flow through the space between them. The electrons cross this space by a process called quantum tunneling, which gives the STM its name. This tiny current of electrons flows when the tip is almost touching the surface. The current changes as the probe moves along the surface. This change is recorded by a computer, which makes it into a picture that we can see.
The surface and the tip must conduct electrons, so they must be made of a metal or semiconductor. A related kind of microscope senses the force instead of the electric current. This kind of microscope is called an atomic force microscope.
STM is a hard thing to do, because it needs a very clean surface and a very sharp needle tip. The STM usually works in a vacuum to keep the air molecules from disturbing the surface, but it can also work in air or water.
First, the tip is brought very close to the surface of thing being studied. This distance is about half of a nanometer. Then the tip is moved very carefully back and forth across the surface. The electrical current is measured while the tip is moved back and forth (constant height method). The STM can also work by adjusting the tip so the tunnel current stays the same (constant current method). Using the constant-height method is faster. Using constant-current method helps avoid bumping the tip into things on the surface, so it can study things that are rougher.
The STM can move an atom (or a molecule) to a new place on the surface. To move an atom, the tip is moved so it touches the atom. Then the tip pulls or pushes the atom to a new place. Moving atoms allows scientists to arrange them into tiny objects, so they can test their properties and try out new ideas.
The parts of an STM are: scanning tip, something that moves the tip, something that stops it from vibrating, and a computer that controls the tip and makes the picture.
Energy level
Simply defined as the different states of potential energy for electrons in an atom. A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. The term energy level is most commonly used in reference to the electron configuration in atoms or molecules. In other words, the energy spectrum can be quantized (see continuous spectrum for the more general case).
As with classical potentials, the potential energy is usually set to zero at infinity, leading to a negative potential energy for bound electron states.
Energy levels are said to be degenerate, if the same energy level is obtained by more than one quantum mechanical state. They are then called degenerate energy levels.
The following sections of this article gives an overview over the most important factors that determine the energy levels of atoms and molecules.
Assume an electron in a given atomic orbital. The energy of its state is mainly determined by the electrostatic interaction of the (negative) electron with the (positive) nucleus. The energy levels of an electron around a nucleus are given by :
where formula_2 is the Rydberg constant (typically between 1 eV and 10 eV), "Z" is the charge of the atom's nucleus, formula_3 is the principal quantum number, "e" is the charge of the electron, formula_4 is Planck's constant, and "c" is the speed of light.
The Rydberg levels depend only on the principal quantum number formula_3.
Fine structure arises from relativistic kinetic energy corrections, spin-orbit coupling (an electrodynamic interaction between the electron's spin and motion and the nucleus's electric field) and the Darwin term (contact term interaction of s-shell electrons inside the nucleus). Typical magnitude formula_6 eV.
Spin-nuclear-spin coupling ("see hyperfine structure"). Typical magnitude formula_7 eV.
If there is more than one electron around the atom, electron-electron-interactions raise the energy level. These interactions are often neglected if the spatial overlap of the electron wavefunctions is low.
The interaction energy is: formula_8 with formula_9
This takes both the magnetic dipole moment due to the orbital angular momentum and the magnetic momentum arising from the electron spin into account.
Due to relativistic effects (Dirac equation), the magnetic moment arising from the electron spin is formula_10 with formula_11 the gyro-magnetic factor (about 2).
formula_12
The interaction energy therefore gets formula_13.
Interaction with an external electric field ("see Stark effect").
Roughly speaking, a molecular energy state, i.e. an eigenstate of the molecular Hamiltonian, is the sum of an electronic, vibrational, rotational, nuclear and translational component, such that:
where formula_15 is an eigenvalue of the electronic molecular Hamiltonian (the value of the potential energy surface) at the equilibrium geometry of the molecule.
The molecular energy levels are labelled by the molecular term symbols.
The specific energies of these components vary with the specific energy state and the substance.
In molecular physics and quantum chemistry, an energy level is a quantized energy of a bound quantum mechanical state.
Crystalline materials are often characterized by a number of important energy levels. The most important ones are the top of the valence band, the bottom of the conduction band, the Fermi energy, the vacuum level, and the energy levels of any defect states in the crystals.
Atomic nucleus