Emission of Light By Atoms - Kilby利用原子-基尔比光发射.docx

THE BOHR MODEL AND THE ATOMIC SPECTRUM OF HYDROGEN(Zumdahl, pp. 284-290)Everyone knows that white light isnt really white; it is a composite of a “rainbow” of colours that blend into one another. If we take white light and split it up using a prism, we form a “continuous spectrum” of colour. In this continuous spectrum, each colour of light has a different amount of energy; red light is much less energetic than violet light.(/astronomy/hp/pix/ce-continuoussplabeled.jpg)If we take atoms and “excite” (cause the electrons to “jump”) them by using a high electrical voltage, light is produced by the gas. If we look at this light through a device called a spectrophotometer, we can see the spectrum of light formed by that particular gas. Instead of a continuous band of colour, you should notice a small number of very sharp bands of colour separated by black space. This type of spectrum is called a “line spectrum” (in this case an emission spectrum) and shows us that the light coming from the gases is made up of only a few different energies.(/afrank/A105/LectureVI/FG04_003_PCT.gif)How are these line spectra produced? In 1911, Niels Bohr hypothesized that the electrons in atoms traveled around the nucleus in orbits that were found at fixed distances from the nucleus. Each of the orbits also corresponded to specific level of energy. The orbit closest to the nucleus was called n = 1, the next n = 2, the next n = 3 and so on. The lowest orbit (the one closest to the nucleus) was also called the “ground state” orbit and represented the lowest energy state. As the “n” number increased, the amount of energy associated with it also increased. Bohr, in studying the spectrum given off by the hydrogen atom, thought that an electron could jump from one energy level to another if it absorbed or emitted just the right amount of energy. In order for an electron to “jump” to a higher orbit, it had to absorb energy from heat or electricity. In this higher (“excited”) state, the electron was unstable and it would eventually fall down to its regular orbit. In falling back down, the electron released (emitted) the energy that it had absorbed in the form of light. This amount of energy corresponded to a specific coloured band in the spectrum for hydrogen.Unfortunately, Bohr could not explain the spectra of elements other than hydrogen using his model. A new model would soon be formed.Significance of the line spectrum of hydrogen?The discrete bands of colour in the line spectrum show that there are only certain energies available to the electron in the hydrogen atom. In 1900, Max Planck, a German physicist, was examining the radiation profiles of solids that had been heated to incandescence. He was unable to explain his observations using known theories, so he devised his own hypothesis:“Energy can be gained or lost only in whole number multiples of the quantity hv, where h is a constant and v is the frequency of the radiation being emitted”Translation: Planck discovered that energy is QUANTIZEDthat is that energy is found in discrete “packages” that he called QUANTA (singular = quantum)Using Plancks theory, we can calculate the size of a quantum of energy for a particular wavelength of light. Mathematically, Plancks theory is:E=hvWhere:E = change in energyh = Plancks constant = 6.626 x 10-34 Jsv = frequency of the radiationIf the frequency is not given in the problem, it can be calculated as follows:v=cWhere:v = frequency of the radiationc = the speed of light (2.9979 x 108m/s = wavelength of the light (must be in m)Sample Exercise 7.2 (p.278 in Zumdahl)The blue colour in fireworks is often achieved by heating copper (I) chloride (CuCl) to about 1200oC. At this temperature, the compound emits blue light having a wavelength of 450 nm. What is the increment of energy (quantum) that is emitted at this wavelength?Einstein eventually took Plancks ideas and applied them to electromagnetic radiation. Einstein hypothesized that electromagnetic radiation was just a stream of particles and that is can also be quantized. Einstein called each quantum of electromagnetic radiation a PHOTON.Using Plancks and Einsteins theories, Bohr was able to calculate the energy available to the hydrogen electron at any of its orbit positions. He then hypothesized that, if the energy of the electron is known for two different orbits, the change in energy (absorbed or released) could be calculated when the electron moves from one orbit to another. E= -2.178 x 10-18J1n(final)2- 1n(initial)2Finally, if the energy absorbed or released by the electron as it moves is know, we can calculate the wavelength of the photon of light that is