England women's national football team
The England women's national football team plays for England in international women's football. The side has been quite successful of late. The team has qualified for five World Cups: 1995, 2007, 2011, 2015 and 2019.
In May 2009, it was announced that a number of the England Women's Team would be awarded central contracts, to help the players concentrate on full-time training and playing, without having to fit it around full-time employment. Seventeen players initially signed contracts.
In 2009, the team reached the European Championships Final, losing 6–2 to Germany. In 2015, the side had their most impressive achievement to date by finishing in third place in the 2015 World Cup.
Group 5
"England squad for 2011 FIFA Women's World Cup qualifiers versus Austria and Spain, 25 March and 1 April 2010, announced 10 March 2010. Players in bold have central contracts."
The following players have also been called up this season.
Planck constant
The Planck constant (Planck's constant) says how much the energy of a photon increases, when the frequency of its electromagnetic wave increases by 1 (In SI Units). It is named after the physicist Max Planck. The Planck constant is a fundamental physical constant. It is written as h.
The Planck constant has dimensions of physical action: energy multiplied by time, or momentum multiplied by distance. In SI units, the Planck constant is expressed in joule seconds (J⋅s) or (N⋅m⋅s) or (kg⋅m⋅s).
The symbols are defined here.
In SI Units the Planck constant is exactly J·s (by definition). Scientists have used this quantity to calculate measurements like the Planck length and the Planck time.
Between 1670 and 1900 scientists discussed the nature of light. Some scientists believed that light consisted of many millions of tiny particles. Other scientists believed that light was a wave.
In 1678, Christiaan Huygens wrote the book "Traité de la lumiere" ("Treatise on light"). He believed that light was made up of waves. He said that light could not be made up of particles because light from two beams do not bounce off each other.
In 1672, Isaac Newton wrote the book "Opticks". He believed that light was made up of red, yellow and blue particles which he called corpusles. Newton explained this by his "two prism experiment". The first prism broke light up into different colours. The second prism merged these colours back into white light.
During the 18th century, Newton's theory was given the most attention. In 1803, Thomas Young described the "double-slit experiment". In this experiment, light going through two narrow slits interferes with itself. This causes a pattern which shows that light is made up of waves. For the rest of the nineteenth century, the wave theory of light was given the most attention. In the 1860s, James Clerk Maxwell developed equations that described electromagnetic radiation as waves.
The theory of electromagnetic radiation treats light, radio waves, microwaves and many other types of wave as the same thing except that they have different wavelengths. The wavelength of the light we can see with our eyes is roughly between 400 and 600 nm. The wavelength of radio waves varies from 10 m to 1500 m and the wavelength of microwaves is about 2 cm. In a vacuum, all electromagnetic waves travel at the speed of light. The frequency of the electromagnetic wave is given by:
The symbols are defined here.
All warm things give off thermal radiation, which is electromagnetic radiation. For most things on Earth this radiation is in the infra-red range, but something very hot (1000 °C or more), gives off visible radiation, that is, light. In the late 1800's many scientists studied the wavelengths of electromagnetic radiation from black-body radiators at different temperatures.
Lord Rayleigh first published the basics of the Rayleigh-Jeans law in 1900. The theory was based on the Kinetic theory of gasses. Sir James Jeans published a more complete theory in 1905. The law relates the quantity and wavelength of electromagnetic energy given off by a black body radiator at different temperatures. The equation describing this is:
For long-wavelength radiation, the results predicted by this equation corresponded well with practical results obtained in a laboratory. However, for short wavelengths (ultraviolet light) the difference between theory and practice were so large that it earned the nickname "the ultra-violet catastrophe".
in 1895 Wien published the results of his studies into the radiation from a black body. His formula was:
This formula worked well for short wavelength electromagnetic radiation, but did not work well with long wavelengths.
In 1900 Max Planck published the results of his studies. He tried to develop an expression for black-body radiation expressed in terms of wavelength by assuming that radiation consisted of small quanta and then to see what happened if the quanta were made infinitely small. (This is a standard mathematical approach). The expression was:
If the wavelength of light is allowed to become very large, then it can be shown that the Raleigh-Jeans and the Planck relationships are almost identical.
He calculated "h" and "k" and found that
The values are close to the modern day accepted values of and respectively. The Planck law agrees well with the experimental data, but its full significance was only appreciated several years later.
It turns out that electrons are dislodged by the photoelectric effect if light reaches a threshold frequency. Below this no electrons can be emitted from the metal. In 1905 Albert Einstein published a paper explaining the effect. Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy. Einstein said that the effect was due to a photon striking an electron. This demonstrated the particle nature of light.
Einstein also found that electromagnetic radiation with a long wavelength had no effect. Einstein said that this was because the "particles" did not have enough energy to disturb the electrons.
Planck suggested that the energy of each photon was related to the photon frequency by the Planck constant. This could be written mathematically as:
Planck received the Nobel Prize in 1918 in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta. In 1921 Einstein received the Nobel Prize for linking the Planck constant to the photoelectric effect.
The Planck constant is of importance in many applications. A few are listed below.
In 1913 Niels Bohr published the Bohr model of the structure of an atom. Bohr said that the angular momentum of the electrons going around the nucleus can only have certain values. These values are given by the equation
where
The Bohr model of the atom can be used to calculate the energy of electrons at each level. Electrons will normally fill up the lowest numbered states of an atom. If the atom receives energy from, for example, an electric current, electrons will be excited into a higher state. The electrons will then drop back to a lower state and will lose their extra energy by giving off a photon. Because the energy levels have specific values, the photons will have specific energy levels. Light emitted in this way can be split into different colours using a prism. Each element has its own pattern. The pattern for neon is shown alongside.
In 1927 Werner Heisenberg published the uncertainty principle. The principle states that it is not possible to make a measurement without disturbing the thing being measured. It also puts a limit on the minimum disturbance caused by making a measurement.