Question

Assume that the de-Broglie was associated with an electron can forma 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 d between the atoms of the array is 2 Å. A similar standing wave is again formed if d is increased to 2.5 Å but not for any intermediate value of d. Find the energy of the electron in eV and the least value of d for which the standing wave of the type described above can form.

Answer 1

From the figure it is clear that

(i) de Broglie wavelength is given by

K = kinetic energy of electron

∴ K = 150.8 eV

 N The least value of d will be when only one loop is formed