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:

The wavelength for hydrogen-like atoms is given by \(1/\lambda \propto Z^2\). For the first transition of the Lyman series (n=1 to n=2), \(lambda_H = 4/(3R)\) and \(lambda_{\text{He}^+} = 1/(3R)\). Their ratio \(lambda_H / \lambda_{\text{He}^+} = 4\). So (A) is true. Reason (R) is false as nuclei are not perfectly fixed; they exhibit recoil and vibration.