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:

Maximum kinetic energy is given by $K = E - W$. For the first radiation, $K_1 = 1.0 - 0.5 = 0.5 eV$. For the second radiation, $K_2 = 2.5 - 0.5 = 2.0 eV$. The ratio of their kinetic energies is $K_1/K_2 = 0.5/2.0 = 1/4$. Since $K \propto v^2$, the ratio of speeds is $v_1/v_2 = \sqrt{K_1/K_2} = \sqrt{1/4} = 1/2$.