Chemistry - Atomic Structure Question with Solution | TestHub

DeBroglie wave length is given as
$\lambda =\frac{\text{h}}{\sqrt{2\text{m}\left(\text{K.E}\right)}}=\frac{\text{h}}{\sqrt{2\text{m}\frac{3}{2}{\text{k}}_{\text{b}}·\text{T}}}=\frac{\text{h}}{\sqrt{{\text{3 k}}_{\text{b}}\text{m T}}}$
${\text{k}}_{\text{b}}$is Boltzmann's constant
${\lambda }_{\text{He}}=\frac{\text{h}}{\sqrt{{\text{3 k}}_{\text{b}}\left(200\right)4\times \text{1.66}\times 10^{-27}}}\}\begin{array}{c}\text{T}=\text{200 K}\\ {\text{m}}_{\text{He}}=4\times \text{1.66}\times 10^{-27}\text{ kgs}\end{array}$
${\lambda }_{\text{Ne}}=\frac{\text{h}}{\sqrt{{\text{3 k}}_{\text{b}}\left(1000\right)20\times \text{1.66}\times 10^{-27}}}\}\begin{array}{c}\text{T}=\text{1000 K}\\ {\text{m}}_{\text{Ne}}=20\times \text{1.66}\times 10^{-27}\text{ kgs}\end{array}$
$\frac{{\lambda }_{\text{He}}}{{\lambda }_{\text{Ne}}}=\sqrt{\frac{1000\times 20}{200\times 4}}=\sqrt{25}=5$