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:

Concept: Special Relativity, velocity addition formula.
Formula: Relativistic velocity addition \(v_{\text{rel}} = \frac{v_1 - v_2}{1 - \frac{v_1 v_2}{c^2}}\) where \(v_1, v_2\) are velocities of two objects.
Solution: For two photons moving in opposite directions (\(v_1 = c, v_2 = -c\)), the relativistic velocity addition formula gives \(v_{\text{rel}} = \frac{c - (-c)}{1 - \frac{c(-c)}{c^2}} = \frac{2c}{1+1} = c\). So (A) is true. The rest mass of a photon is zero, which is the reason why photons always travel at the speed of light \(c\) in all inertial frames, forming the foundation of special relativity. Thus, (R) explains the relativistic behavior described in (A).