The de Broglie wavelength (λ) associated with a photoelectron...

According to de-Broglie wavelength equation, $$\lambda=\frac{h}{m v} \Rightarrow \lambda \propto \frac{1}{v}$$ 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 \quad \lambda \propto \frac{1}{\left(\mathrm{v}-\mathrm{v}_{0}\right)^{1 / 2}} \end{array}