Assume that the de Broglie wave associated with an electron can from a standing wave between the atom arrange in a one dimensional array with nodes at each of the atomic sites. It is found that one such standing wave if the distance d between the atoms of the array is `2 A^0` A similar standing wave is again formed if d is increased to `2.5Å` . Find the energy of the electrons in electron volts and the least value of d for which the standing wave type described above can from .

Answer

A

Explanation

From the theory of standing weve, we can say that
`(lambda)/(2) = (2.5 - 2.0) = 0.5 Å`
or `lambda = 1 Å`


Therefore, least value of d required will
correspond to a single loop.
`:. d_(min) = (lambda)/(2) = 0.5 Å`
Further for de-Broglie wavelength of an electron,
`lambda = sqrt((150)/(K(in eV)) Å`
`lambda =1 Å`
`:. K = 150 eV`.