Chemistry - Atomic Structure Question with Solution | TestHub

According to de-Broglie wavelength equation, $$\lambda =\frac{h}{mv}\Rightarrow \lambda \propto \frac{1}{v}$$ According to photoelectric effect, $$\begin{array}{l}\mathrm{hv}-{\mathrm{hv}}_0=\frac{1}{2}{\mathrm{mv}}^2;\mathrm{v}-{\mathrm{v}}_0=\frac{1}{2}=\frac{{\mathrm{mv}}^2}{\mathrm{h}}\\ \mathrm{v}-{\mathrm{v}}_0\propto {\mathrm{v}}^2\\ \mathrm{v}\propto {\left(\mathrm{v}-{\mathrm{v}}_0\right)}^{1/2}\\ \therefore \lambda \propto \frac{1}{{\left(\mathrm{v}-{\mathrm{v}}_0\right)}^{1/2}}\end{array}$$