How did the wave picture of the electron save Bohrs theory?
Once it became apparent that the electron must have a wavelike character, things began to fall into place. The possible states of an electron confined to a fixed space are in many ways analogous to the allowed states of a vibrating guitar string. These states are described as standing waves that must possess integral numbers of nodes. The states of vibration of the string are described by a series of integral numbers n = 1,2,… which we call the fundamental, first overtone, second overtone, etc. The energy of vibration is proportional to n2. Each mode of vibration contains one more complete wave than the one below it. In exactly the same way, the mathematical function that defines the probability of finding the electron at any given location within a confined space possesses n peaks and corresponds to states in which the energy is proportional to n2. The electron in a hydrogen atom is bound to the nucleus by its spherically symmetrical electrostatic charge, and should therefore exhibi
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