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:

Initially, $\frac{1}{2}mv^2 = \frac{hc}{\lambda} - W$ . Finally, $\frac{1}{2}mv'^2 = \frac{hc}{3\lambda/4} - W = \frac{4hc}{3\lambda} - W$ . This can be rewritten as $\frac{1}{2}mv'^2 = \frac{4}{3}(\frac{hc}{\lambda} - W) + \frac{W}{3} = \frac{4}{3}(\frac{1}{2}mv^2) + \frac{W}{3}$ . Since $W$ is positive, $\frac{1}{2}mv'^2 > \frac{4}{3}(\frac{1}{2}mv^2)$ , meaning $v'^2 > \frac{4}{3}v^2$ or $v' > \sqrt{\frac{4}{3}}v$ .