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:

From Einstein's photoelectric equation, $K_{max} = h\nu_{incident} - h\nu_{threshold}$. Here, incident frequency is $2\nu$ and threshold frequency is $\nu$. So, $K_{max} = h(2\nu) - h\nu = h\nu$. Since $K_{max} = \frac{1}{2}mv^2$, we have $\frac{1}{2}mv^2 = h\nu \implies v^2 = \frac{2h\nu}{m} \implies v = \sqrt{\frac{2h\nu}{m}}$.