Grating Spectrometer.doc
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1、PHYS 2211LLAB 19The Grating Spectrometer and the Rydberg ConstantPurposeLight carries an extraordinary amount of information. Beyond its ability to form images, the mixture of wavelengths the spectrum of which light is usually composed can tell us a great deal about distant or inaccessible objects.
2、It is by examining spectra that we have been able to determine such things as the structure of atoms, the composition of stars, the velocities of galaxies, even the age of the universe.The tool for doing this is the spectrometer. In this lab we will use a grating spectrometer to measure the waveleng
3、ths of light emitted by several elements and to identify an unknown gas. We will also use it to take a peak inside the hydrogen atom and “weigh” its electron.PrinciplesThe grating spectrometer consists of a diffraction grating set behind a narrow slit. Light passing through the slit and the grating
4、is diffracted at an angle that depends on its wavelength. Red light (long wavelengths) will emerge from the grating at larger angles than blue light (shorter wavelengths). The observer sees a separate image of the slit for each wavelength (color) in the light.The set of wavelengths in the light from
5、 an object is called its spectrum. There are two general types of spectra: continuous and discrete. In a continuous spectrum, there is a complete range of wavelengths so that the colors gradually pass from blue to red. A rainbow is a continuous spectrum created by water droplets in the air. (The dro
6、ps act as small prisms prisms will also diffract light according to wavelength.)In a discrete spectrum, only selected wavelengths are represented. The light from a neon sign is a selection of discrete wavelengths. Our eyes average these out into a single color, but a spectrometer displays each wavel
7、ength individually.How light is generatedIt will be helpful to consider how light is generated. Matter is made of charged particles electrons and protons, which together with neutrons form atoms and molecules. When charged particles vibrate, they emit electromagnetic radiation light. (We will call a
8、ny EM radiation “light”, even though it may not be in the visible range of frequencies.)The light waves generated by charged particles will have the same frequency as their frequency of vibration. The wavelength of the light is inversely related to the frequency. (Recall that the speed of a wave is
9、its wavelength times its frequency: v = f. Since the speed of light is fixed, the wavelength is determined by =v/f.)One mechanism of light generation is called thermal radiation. All atoms and molecules are continually vibrating or colliding with each other, at frequencies determined by their temper
10、ature. Because of the random nature of their motions, there is a complete range of frequencies involved, and so a continuous spectrum of light is generated.A second mechanism involves the shifting of electrons between energy levels inside an atom. Each atom in nature has a unique configuration of en
11、ergy levels in which the electrons of the atom reside. When an atom receives a kick of energy for instance by a collision with another atom one or more of its electrons will shift to a higher energy level. To return to its “ground” state, the electron must give up this extra energy, and it does so b
12、y emitting light. The wavelength of the light depends on the difference in energy between the two levels.If we excite an elemental gas for instance neon at any given time there will be many electrons undergoing all possible energy level shifts. Since there is a discrete (i. e., countable) number of
13、possible shifts, a discrete spectrum of light will be given off by the gas. This is what the neon in a neon sign is doing, and this is what we will observe with the spectrometers.The Hydrogen Spectrum and the Rydberg ConstantSince the beginning of spectroscopy in the 19th century, scientists have no
14、ted patterns in the spectral lines of the elements. (The image of the spectroscopes slit looks like a line of light, so different wavelengths are commonly called “lines”.) The four lines in the visible spectrum of hydrogen can be quantified by the empirical formula(n = 3, 4, 5, 6)RH = 1.097 x 107 m-
15、1RH is called the Rydberg Constant (for hydrogen) The above is called the Balmer formula and refers to the visible lines in the spectrum. If we include infrared and ultraviolet lines, the formula can be generalized to(1)These patterns were mysterious at first, but we now know they are clues to the i
16、nternal structure of atoms. The ns refer to the energy levels of the atom, with the lowest energy level (the ground state) being labeled n = 1. As an electron drops from a high energy level (labeled by ni to a lower state, labeled by nf, it will emit light of wavelength .The Bohr Model of the Hydrog
17、en AtomMaking the connection between the above empirical formula and the internal structure of an atom took all the tricks in the classical physicists bag from mechanics through electrodynamics and optics as well as some new ideas that came to be known as quantum mechanics.The story can be outlined
18、briefly. First, in studying thermal radiation, the physicist Max Planck found that its spectrum could be understood only if it were postulated that the energy of radiation was proportional to its frequency, E = hf(h = 6.626 x 10-34 J-sec)and that the energy stored at a given frequency in an electrom
19、agnetic field had to be an integer multiple of a fundamental energy: Efield = nhf, with n integer. The constant h is known as Plancks constant. This was the origin of the idea of the quantum that energy comes in discrete dollops rather than continuously.Einstein carried the story further by proposin
20、g that light, although it travels as a wave, is emitted and absorbed by electrons in discrete packets, now called photons. By identifying these photons with Plancks quanta, he was able to successfully explain the photoelectric effect.Finally, Niels Bohr applied these ideas to the hydrogen atom, and
21、added a few ideas of his own. It was known that the hydrogen atom contained a negative charge in the form of an electron, and a positive charge in the form of a nucleus (a proton), but it was a mystery how the two could form a stable configuration without falling into each other. If the electron sim
22、ply orbited the nucleus like a planet around the Sun, it would quickly radiate away its energy and fall into the nucleus. (It is well established that all accelerating charges radiate, and the electron is no exception. The glow of a light bulb comes from the acceleration of electrons.)Bohr proposed
23、that the electron did indeed orbit the nucleus, but that its angular momentum is quantized, so that the electron is fundamentally restricted to certain discrete values of angular momentum. He showed that these allowed values had to be proportional to Plancks constant h, so Bohr postulate wasL = n (n
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