CAPÍTULO 3. EVALUACIÓN DE LAS MEDIDAS OBJETIVAS DE CALIDAD
A. Almacenamiento
Since theoretical work undergone by James Clerk Maxwell between 1861 and 186540 and, later, the experimental observations by Heinrich Hertz in 1887 – 1888,41light is described as oscillations of electric and magnetic fields perpendicular to each other.40,41 More pre- cisely, light can be seen as a propagating electromagnetic wave, hence “light” is sometimes referred to as electromagnetic radiation. The electromagnetic wave is characterised by its frequency (ν, the number of wave cycles completed per unit of time) and its wavelength
Figure 1.4: The electromagnetic spectrum with approximate wavelength,λ, and frequency,
ν, values for each radiation category. The visible range of the spectrum, ∼ 380 – 780
nanometres (nm, 10-9 metres), and the colours associated with these wavelengths is pre- sented in greater detail.
tities are related to each other by the speed of light (in vacuum),c≈2.998×108 metres per second (m·s−1), by c = λν. The electromagnetic spectrum, shown in Figure 1.4, corresponds to the range of possible frequencies of electromagnetic radiation. In order of increasing wavelength (decreasing frequency), electromagnetic radiation can be classified in seven broad categories: γ-rays, X-rays, ultraviolet (UV), visible (Vis), infrared (IR), microwaves and radio waves.42
Any physical object can emit electromagnetic radiation. For a black–body,i.e. an ide- alised object which is capable of absorbing and emitting all wavelengths of radiation, the peak wavelength of the emitted radiation shifts to shorter wavelengths as its temperature,
T, is increased, as shown in Figure 1.5.42,43Drawing on classical principles, Lord Rayleigh proposed a model for black–body radiation which reasonably predicted the emission spec- trum at long wavelengths but failed for shorter wavelengths (see Figure 1.5). In fact, the
Rayleigh–Jeans law implies that even objects at room temperature would emit UV (and even higher energy) radiation. This obviously nonsensical result is famously known as the “ultraviolet catastrophe”.42,43
In 1901, Max Planck presented an alternative description of black–body radiation for which the ultraviolet catastrophe was not a concern.44A constant term arose from Planck's work on black–body radiation, so that the energy of electromagnetic radiation would be
7 x 1 0 - 7 1 x 1 0 - 6 2 x 1 0 - 6 3 x 1 0 - 6 4 x 1 0 - 6
B
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W
a v e l e n g t h / m
T = 2 0 0 0 K T = 2 5 0 0 K T = 3 0 0 0 K T = 3 5 0 0 K T = 4 0 0 0 K T = 4 5 0 0 K T = 5 0 0 0 K R a y l e i g h - J e a n s l a w ( a t 4 5 0 0 K )Figure 1.5: Emission spectra from an idealised black–body at different temperatures (in- creasingly darker blue lines for increasing temperature). The spectra were produced by employing Planck’s law (closest to experimental observation), which defines black–body radiation emission as 8πhc/λ5(ehc/λkT −1). For comparison, the Rayleigh-Jeans law for a blackbody at 4500 K was also produced (pink dashed line, compared with its equiva- lent under Planck’s law in the pink solid line). According to the Rayleigh-Jeans law the black–body radiation emission is modelled by 8πkT /λ4. Notice that the Rayleigh-Jeans law follows the same trend as Planck’s law for long wavelengths but quickly deviates and thus fails to accurately predict black–body radiation emission at higher energies.
given by:
E =hν (1.2)
whereh is Planck's constant,h = 6.626×10−34Joules×seconds (Js). The implications of this result were only fully understood in 1905, when Einstein interpreted the ‘pioneering work by Mr. Lenard’ on photoelectric phenomena in light of Planck's ideas.45 These photoelectric phenomena related to the observation that, when irradiating metals with ultraviolet radiation, the ejection of an electron is independent from the light's intensity but highly dependent on the radiation’s frequency.42 Particularly, no electrons are ejected until a certain threshold frequency (characteristic to each metal) is reached, and above this threshold the kinetic energy of ejected electrons increases linearly with increasing frequency of incident radiation. To provide an explanation for these observations, Einstein reasoned that light would be composed of energy quanta, i.e. a “packet” of energy, or particle of light, now known as a photon.45 Assuming a photon collides with an electron to eject it, for the energy to be conserved the kinetic energy of the electron, eKE, must be defined by:
eKE = 1 2mev
whereme is the mass of the electron,vits velocity,hν is the energy of the photon andW is called thework function,i.e. the threshold energy necessary to eject an electron from a certain metal.42,45This relationship, now commonly referred to as thephotoelectric effect, predicts both the proportionality between eKE and ν, and the impossibility of electron ejection when hν < W (since this implies eKE < 0). The existence of photons — or, in other words, the particle character of electromagnetic radiation — was thus proven. Note, however, that the particle-like behaviour of light demonstrated by Einstein does not invalidate its wave-like characteristics: it remains true that, once directed at a set of double slits, a beam of light will produce a diffraction pattern, a characteristic behaviour of a wave.
It is important to expand on this point to mention that, in light of the aforementioned conclusions for photons, Louis de Broglie suggested in his doctoral thesis of 1924 that electrons (commonly regarded as particles) would demonstrate wave-like behaviour un- der certain conditions.46 He then defined the de Broglie wavelength, i.e. the wavelength associated with the wave character of a particle, as:
λdeBroglie = h
p =
h
mv (1.4)
withpbeing the momentum of the particle. Experimental evidence for de Broglie's theories was gathered in the Davisson–Germer experiment of 1928, where an electron beam was observed to produce a diffraction pattern akin to that observed for waves of light and with wavelengths comparable to the theoretical de Broglie wavelength.47 It was then concluded that both matter and radiation can demonstrate either wave- or particle-like characteristics, depending on the experimental conditions; this is now known as thewave- particle duality.48