Each line can be calculated from a combination of simple whole numbers. The lines in the hydrogen emission spectrum form regular patterns and can be represented by a (relatively) simple equation. The origin of the hydrogen emission spectrum The various combinations of numbers that can be substituted into this formula allow the calculation the wavelength of any of the lines in the hydrogen emission spectrum there is close agreement between the wavelengths generated by this formula and those observed in a real spectrum.Ī modified version of the Rydberg equation can be used to calculate the frequency of each of the lines: In other words, if \(n_1\) is, say, 2 then \(n_2\) can be any whole number between 3 and infinity. \(n_1\) and \(n_2\) are integers (whole numbers).The Lyman Series involves transitions down to the n = 1 orbit and involve higher frequency photons in the UV region whilst the Paschen Series (to n = 3) produces IR spectral lines.\right)\] This is shown schematically in the diagram below for the Bohr model of the atom. The Balmer series of visible lines for atomic hydrogen are caused by transitions from the n = 2 orbit to and from higher orbits. This photon, however, could be emitted in any direction, not just in the same direction as the original incident photon. The electron then "de-excites" and jumps back down to a lower energy orbit, emitting a photon of specific frequency. The photon is absorbed by the electron so cannot continue on to be detected by an observer. If a photon of a specific frequency interacts with the electron, it can gain sufficient energy to "jump up" one or more levels. The energy of a photon is a function of its frequency and is determined by:Į = h f where f is the frequency of the photon, E is the energy and h is Planck's constant (= 6.626 x 10 -34J.s)Īn electron orbit a nucleus in a stable energy level. Photons of light each have a specific frequency. These two types are in fact related and arise due to quantum mechanical interactions between electrons orbiting atoms and photons of light. Line spectra appear in two forms, absorption spectra, showing dark lines on a bright background, and emission spectra with bright lines on a dark or black background. A 10,000 K star appears blue-white whilst a 3,000 K star appears red. Not only does the shape of the curve determine the relative intensity of the different components of the continuous spectrum produced by the star, it also determines the colour of the star. You can see clearly from the plot that a 10,000 K star would have its peak wavelength in the ultraviolet part of the em spectrum whilst a 3,000 K star would emit most of its radiation in the infrared part. Normalised plots for 6 different black bodies. The plot below shows a Planck curve for an object with a 6,000 K effective temperature, the same temperature as the Sun. This plot is called the blackbody curve or the Planck curve, after the German physicist Max Planck who first postulated that electromagnetic radiation was quantised. The continuous spectrum produced by a black body is distinctive and can be shown as an intensity plot of intensity against emitted wavelength. Examples of such objects include the tungsten filaments of incandescent lamps and the cores of stars. These must be sources of thermal energy and must be sufficiently opaque that light interacts with the material inside the source. In the real world some objects approximate the behaviour of blackbodies. As it absorbs energy it heats up and re-radiates the energy as electromagnetic radiation. This sphere approximates what physicists call a black body.Ī black body radiator is a theoretical object that is totally absorbent to all thermal energy that falls on it, thus it does not reflect any light so appears black. If you were able to keep heating it sufficiently it may even glow blue hot. As you continue heating it the sphere glows first red, then orange, yellow then white hot. Applying the torch again puts more energy into the sphere - it gets hotter. When you remove the torch you can feel the heat being re-radiated by the sphere. What gives rise to a continuous spectrum? Imagine heating a solid steel sphere with a blowtorch. Specific examples are discussed on another page. Astronomical spectra can be combination of absorption and emission lines on a continuous background spectrum. This is particularly relevant in astronomy and is discussed in the next section. One means by which a continuous spectrum can be produced is by thermal emission from a black body. Simple examples in the visible wavebands are shown below. Spectra can be simplified to one of three basic types.
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