Photoelectric Effects and deBroglie Equation: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Photoelectric Effects and deBroglie Equation. Understanding the underlying formula is key to arriving at the correct answer below:

Since work function is negligible, the kinetic energy of the electron is $K = \frac{hc}{\lambda}$. The de-Broglie wavelength of the electron is $\lambda_d = \frac{h}{\sqrt{2mK}}$. Squaring both sides gives $\lambda_d^2 = \frac{h^2}{2m(hc/\lambda)} = \frac{h\lambda}{2mc}$. Rearranging for $\lambda$ yields $\lambda = \left(\frac{2mc}{h}\right)\lambda_d^2$.