Question

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 $d$ between the atoms of the array is $2\mathring{A}$. A similar standing wave is again formed, if $d$ is increased to $2.5\mathring{A}$ but not for any intermediate value of $d$.
Find wavelength of the beam.

• A. $1\mathring{A}$
• B. $2\mathring{A}$
• C. $3\mathring{A}$
• D. $0.5\mathring{A}$

Answer 1

Answer: (A)

From the figure, it is clear that

$p\cdot (\lambda /2)=2\mathring{A}$
$\Rightarrow (p+1)\cdot \lambda /2=2.5\mathring{A}$
$\therefore \lambda /2=(2.5-2.0)\mathring{A}=0.5\mathring{A}$
or $\lambda =1\mathring{A}$