Week 7b - Dual - Nature of Light It is now recognised that...

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Unformatted text preview: Dual - Nature of Light It is now recognised that light has a dual-nature. Light can be considered as a particle or a wave - we never need to use both to describe an effect- only one, as each is mutually incompatible. We will discuss this in more detail later. Quantum Nature of Atoms Hydrogen Spectrum Atomic hydrogen is the simplest atom and is therefore the easiest to study. The emission spectrum of hydrogen exhibits sharp features (called spectral lines) in contrast to the continuous emission of hot bodies. One group of spectral lines lie in the visible region of the E.M. spectrum and is called the Balmer series. % (nm) 300 400 500 600 700 Hydrogen Spectrum J.J. Balmer (1885) showed empirically that all the observed spectral lines in the visible can be ftted to the simple Formula R- was chosen to give the best ft. 1 ! = R 1 2 2- 1 n 2 n = 3,4,5 ...... where R = 1.0968 x 10-3 -1 ! Rydberg's Constant. Hydrogen also emits other spectral lines in the ultraviolet and infrared. These can be Ftted by a similar set of formulae and so on (other series in infrared). 1 ! = R 1 1 2- 1 n 2 n = 2,3,4,5 ...... (Lyman Series - U.V.) and 1 ! = R 1 3 2- 1 n 2 n = 4,5,6 ...... (Paschen Series I.R.) Thompson Model of the Atom (Plum Pudding Model) + ve charge spread through out the atom with the light -ve charge electrons embedded in it. Electrons RUTHERFORD S ATOM In 1911, Rutherford proposed that the mass of an atom is essentially concentrated in a minute very dense nucleus (radius ~ 10-14 m). The positive charge is conned to the nucleus which binds sufcient electrons to it under Coulomb attraction to make the atom overall neutral in charge. Thus a H-atom consists of one positive charge (on a particle called a proton) binding a single electron. The electrons circulate about the nucleus in a volume of radius ~ 10-10 m. HOW DID RUTHERFORD COME TO THE CONCLUSION THAT MOST OF THE MASS OF THE ATOM WAS CONTAINED IN A SMALL VOLUME CALLED THE NUCLEUS? 10 6 232 58 The effect of the cloud of +ve charge would be very small since the mass distribution over the volume of the atom would give rise to a very small density of charge and mass. The possibility of multiple scattering building up to a 180 degree deFection is extremely small, normally a deviation by one collision would be "cancelled" by that of another collision. Classical Theory of the H-atom The centripetal force maintaining the electron in its circular orbit is supplied by the Coulomb force. Assume 1. Circular motion of the electron around the proton. 2. Proton is stationary i.e. F c = mv 2 r = 1 4 ! ! o e 2 r 2 putting k = 1 4 ! ! o ! mv 2 = ke 2 r . Hence , v = ke 2 mr ! mv 2 = ke 2 r . Assuming the proton to be stationary, the total energy of the system is E = K.E.(e) + U(potential energy of p-e system) = 1 / 2 mv 2 + V(-e)....
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Week 7b - Dual - Nature of Light It is now recognised that...

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