c
\(\frac{\mathrm{hc}}{\lambda}=\mathrm{k}_{\max }+\phi[\) given \(\phi\) is negligible \(]\)

\(\text { So, } \frac{h c}{\lambda}=K_{\max }\)

\(\lambda_{d}=\frac{h}{\sqrt{2 m K_{\max }}} \Rightarrow K_{\max }=\frac{h^{2}}{2 m \lambda_{d}^{2}}\)

\(\left(\frac{h c}{\lambda}\right)=\frac{h^{2}}{2 m \lambda_{d}^{2}} \Rightarrow \lambda=\left(\frac{2 m c}{h}\right) \lambda_{d}^{2}\)