De Broglie used Einstein’s special theory of relatively together with Plank’s quantum theory to establish the wave property of particles. He gave fundamental relationship $\large\frac{ \lambda h}{p}$; where $lambda$ and $p$ are wavelength and momentum respectively and $h$ is Plank’s constant. A de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with node at each of the atomic sites. A standing wave is formed when the distance between the atoms of any array is $d = 3A^{\circ}$. A similar standing wave is again formed if $d = 3.5 A^:{\circ}$ but not for any intermediate value of $d$. For thermal neutron at ordinary temperature, energy is given by relation $E = kT$, where $K$ is Boltzmann constant mass of Neutron is $1.67\times10^{–23} g$. The least value of d for which standing wave can be formed is

Question

$\begin {array} {1 1} (a)\;3 \: A^{\circ} & \quad (b)\;0.5\: A^{\circ} \\ (c)\;1\: A^{\circ} & \quad (d)\;1.5\: A^{\circ} \end {array}$