標題:
[chemistry]convergence limit at the end of a spectrum
發問:
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1. explaine why there is a convergence limit at the end of a spectrum
最佳解答:
This is more a physics problem than a chemistry problem because it invloves quantum theory. Since the frequency of electromagnetic wave (EM wave) f given out from a transistion of orbitual electrons from energy level n to a lower level, say a, is given by h.f = k[1/a^2-1/n^2] where h is Planck's constant k is a constant determined by the structure of the atom. Transition from the nect higher level, n+1, down to energy level a, is again given by h.f' = k[1/a^2-1/(n+1)^2] Thus, the difference in frequency (f'-f) is, f'-f = (k/h).[1/n^2-1/(n+1)^2] After some algebric manipulation, it can be shown that f'-f =(k/h)[(2n+1)/(n+1)^2.n^2] When n is large, (2n+1) approximates to 2n and (n+1) approximates to n, then, f'-f =(k/h)[2/n^3] Therefore, the difference in frequency of the emitted EM wave tends to zero when n approaches infinity (very large), which gives a limit to the emitted frequency spectrum. Simply speaking, the physical phenomenon is that for electrons at higher orbits, the difference in energy betweenthe two is negligibly small, which would give mor or less the same energy to the emitted EM wave during transition to lower orbits.
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