Quantum staircase analogy

Figure 7.9 Quantum staircase. In this analogy for the energy levels of the hydrogen atom, an electron can absorb a photon and jump up to a higher step (stationary state) or emit a photon and jump down to a lower one. But the electron cannot lie between two steps.

Figure 7.9 A quantum "staircase" as an analogy for atomic energy levels. Note...

The quantum levels of an electron bound to an atom are cmdely analogous to the gravitational potential energies available to a ball on a staircase. As illustrated in Figure 7-12. a ball may sit on any of the steps. If we define the top of the steps to be 5" = 0, the ball has a negative potential energy when it is on any of the lower steps. To move a ball from the bottom of the staircase to step 5 requires the addition of a specific amount of energy,... 

Quantum mechanics is a highly mathematical view of the atom and expands the classical physics viewpoint to explain atomic structure. A staircase is a useful analogy in discussing quanta, in that you climb the stairs in certain quanta or in certain discrete units, namely, the steps themselves. You cannot step anywhere other than on a stair tread, and standing in between steps is not possible. In the same way, electrons have certain permitted locations and cannot exist between these locations. 

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