By Steven N. Durlauf and Lawrence E. Blume
Read or Download The New Palgrave Dictionary of Economics, Second Edition: Volume 7 PDF
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Extra info for The New Palgrave Dictionary of Economics, Second Edition: Volume 7
The states n 2 3 4 correspond to the excited states of the atom, since their energies are greater than the ground state energy. When the quantum number n is very large, n *, the atom’s radius rn will also be very large but the energy values go to zero, E n 0. This means that the proton and the electron are infinitely far away from one another and hence they are no longer bound; the atom is ionized. In this case there is no restriction on the amount of kinetic energy the electron can take, for it is free.
It must therefore lose energy. The radius of the orbit should then decrease continuously (spiral motion) until the electron collapses onto the nucleus; the typical time for such a collapse is about 108 s. Second, since the frequency of the radiated energy is the same as the orbiting frequency, and as the electron orbit collapses, its orbiting frequency increases continuously. Thus, the spectrum of the radiation emitted by the atom should be continuous. These two conclusions completely disagree with experiment, since atoms are stable and radiate energy over discrete frequency ranges.
If it comes into contact with an atom’s electron, it will interact according to one of the following scenarios: – If it has enough energy, it will knock the electron completely out of the atom and then vanish, for it transmits all its energy to the electron. This is the photoelectric effect. – If its energy hF is not sufficient to knock out the electron altogether, it will kick the electron to a higher orbit, provided hF is equal to the energy difference between the initial and final orbits: hF E n E m .