Problem

Problem

Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one-dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed if the distance dd between the atoms of the array is 2 A˚2 \text{ \AA}. A similar standing wave is again formed if dd is increased to 2.5 A˚2.5 \text{ \AA} but not for any intermediate value of dd. Find the energy of the electron in eV and the least value of dd for which the standing wave of the type described above can form.

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