Earlier we learned that hot, opaque objects produce continuous spectra of radiation of different wavelengths.

Transcription

1 Section7: The Bohr Atom Earlier we learned that hot, opaque objects produce continuous spectra of radiation of different wavelengths. Continuous Spectrum Everyone has seen the spectrum produced when white light passes through a prism. It is a continuous colored band with one color merging into another. 1

2 If we pass the light emitted by an incandescent light bulb through a lens, prism, spectroscope or diffraction grating, it would produce a continuous spectrum (ie. a full range of colors) that contains light of all wavelengths. This spectrum was assumed to be due to the interactions between atoms or molecules and its neighbors. 2

3 There is another type of spectrum called a line spectrum. One way to produce line spectra is to "excite" a gas by passing electricity through it. When conditions are right, the gas will emit light in particular frequencies. You will not see colors merging into one another, but rather you will see distinct colored lines. 3

4 Rarefied gas Atoms in the gas are very far apart. When a rarefied gas under low pressure in a vacuum tube is excited by a voltage between the electrodes at the end of the tube, the atoms become excited. As a result, the electrons are repeatedly bumped to high levels and fall back to lower orbits at which point they emit radiation. We see this radiation as a glow. Hydrogen gas, for example will emit a pink glow. When this light is passed through lenses, a slit, a prism or diffraction grating, and we see the lines mentioned earlier. The emission spectrum for hydrogen is found to exist of 4 lines of visible light: red, blue green, blue and violet. (These lines are actually the image of the slit.) 4

5 Absorption Spectrum If white light is allowed to pass through a gas and the transmitted light is analyzed with a spectroscope, dark lines of missing light are observed in the continuous spectrum at exactly the same frequencies as the lines in the emission spectrum of that gas. This is called an absorption spectrum, created by light absorbed from the continuous spectrum as it passed through the gas. (In other words, atoms absorb light of the same frequencies they emit. 5

6 These sharp colored lines at specific places in the spectrum suggest that there is something going on in the atom that is allowing only certain frequencies to be emitted. (i.e., certain discrete frequencies). It appears that instead of the electron gradually spiralling into the nucleus, it makes certain jumps only say from one orbit to another giving out a particular frequency as it "falls". 6

7 These observations were a mystery until Niels Bohr introduced a new model of the Hydrogen atom. He determined that an electron emits energy (photon) when it drops from a higher energy level to a lower energy level and the Hydrogen atom emits photons at very specific energies. This effect suggests that energy at the atomic level is quantized. 7

8 Niels Bohr ( ) said a shocking thing: he said that the classical ideas of physics cannot be applied to orbiting electrons. Here is a summary of what he said: Of all the possible orbits that electrons might take around a nucleus, only certain orbits are "allowed". For each of those allowed orbits the electron has a specific amount of energy. While it stays in an orbit, the electron will not radiate energy even though it is accelerating! Each orbit is a stationary state. Electrons lose energy only when they "jump" from a higher energy orbit to a lower energy orbit. The difference in the energies of the two orbits is radiated as one photon of electromagnetic radiation. Similarly, an electron can be "bumped" up to a higher energy level only if the atom absorbs a photon whose energy is exactly equal to the energy difference between the two orbits. So Bohr's model gives us an atom with certain stationary states that are characterized by certain allowed orbits of the electrons. The energy level of the electron depends on which orbit it is in. Energy is radiated (or absorbed) only when the electron falls (or is bumped up) to another orbit level. 8

9 Bohr Radius Equation Recall, Bohr was able to show that only certain electron orbits are allowed. That is, he applied the quantum idea to the orbits and concluded that an orbit could only exist if its circumference is some whole number multiple of the de Broglie matter wave (λ = h/mv) associated with the electron. The theoretical radius of the orbit of an electron is given by r n = (5.29 x m) n 2, where, n is the quantum number (orbital number). As you can see a Bohr radius is directly proportional to the square of the quantum number associated with the radius. The energy of an electron orbiting a nucleus as a function of the quantum number (n) (that is, the number of its energy level or orbit) is given by: The electron experiences the greatest force in the first (n = 1) or smallest orbit (due to the Coulomb force of attraction which exists between the proton and electron) which is the smallest orbit (n = 1). It will also have its greatest energy at the first energy level (the smallest orbit). This makes sense because it is in this orbit that the centripetal force is greatest (due to the Coulomb force). As the electron moves in orbits further and further from the positive proton in the nucleus, the Coulomb force or centripetal force becomes smaller. The electron will have zero energy, if the electron moves very far away, say to infinity. 9

10 Energy must be put into the atom to "excite" the electron to higher energy levels. Energy has to be put into the atom to excite the electrons to higher orbits. And if the electron is bumped far enough away from the nucleus, its energy goes to zero. Well, if adding energy makes the energy of the electron go to zero, the electron must have had NEGATIVE energy. Think about a simple case: if adding 3.0 J to an electron makes the energy go to zero, then the energy that the electron already had must have been 3.0 J. 10