Why is the sky blue?
The power of light radiated by an oscillating charge is dependent on the frequency of oscillation. Hence the power radiated by the atom is de atom does not retain the energy provided by incident light as internal energy, the power of light radiated must be exactly the power of light taken from the incident beam in the first place. We conclude the power of light scattered from the incident beam of light is dependent on its own frequency. Air molecules tend to scatter light which matches the natural oscillating frequencies of the molecules. For most air molecules, their natural frequencies electromagnetic spectrum. So visible light and the blue end of the spectrum has a greater tendency to be scattered. We will see that the higher the frequency of light and the closer it is to the natural frequency of the atom the greater the power scattered. pendent on the frequency of the incident light. Since the lie in the ultraviolet region in the
While this is a description of the interaction between light and a single atom, this applies to simple molecules in general, differing in mathematical detail.
The following is a mathematical description of the int be proved that
eraction between single atoms and light. It will
(1) Atoms become oscillating dipoles under light (2) The radiation of light by the oscillating dipole balances the contribution of the incident light. (3) Reradiated light has the same frequency as the i (4) The intensity of light scattered increases when the frequency of light increases and approaches the atom’s natural frequency. There are a few assumptions to be made. Firstly, the atomic model is simplified to have only one resonant frequency. In real life atoms respond to several discrete frequencies. Secondly, the electron cloud is assumed to have uniform charge density, which is an inaccurate description, but it allows us to model the atom as a spring. Thirdly, the atoms are assumed to be the electron cloud is assumed to oscillate about a stationary nucleus. This is justifiable because the nucleus is massive compared to the electrons (a proton or neutron is 1840 times heavier than an electron) and thus it experiences practically negligible influence under the force of light. ncident light. small and independent. 205 Finally
x be the displacement of the centre of the electron
Now consider the motion of the electron cloud. Let cloud and m be the cloud’s mass. By Newton’s second law,
(1)
The next step is to express the forces on the right hand side of the equation as functions of time. The coulomb attraction corresponds to the restoring force of the imaginary spring. that the nucleus never leaves the bounds of the electron cloud, oth torn apart under light. The attraction felt by the positive 206 It can be assumed erwise atoms would be violently nucleus inside electron cloud is
(2)
205 Lipson, S. G., and H. Lipson. ‘13 The Classical Theory of Dispersion.’ Optical Ph 1969. 469-503. Print. 206 Akhmanov, S. A., and S. Yu. Nikitin. ‘5.3 The Classical Model of the Atom.’ Physical Optics. Oxford: Clarendon, 1997. 68-9. Print. ysics. London: Cambridge U.P.,
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