The correct option is **C. The photoelectric effect**. ### Detailed Explanation **1. Understanding Quantum Mechanics vs. Classical Physics:** - **Classical Physics** deals with macroscopic phenomena and is governed by laws such as Newton's laws of motion, thermodynamics, and electromagnetism. It effectively describes the behavior of large objects and systems. - **Quantum Mechanics**, on the other hand, is the branch of physics that deals with phenomena at very small scales, such as atoms and subatomic particles. It introduces concepts like wave-particle duality, quantization of energy, and the uncertainty principle. **2. Analyzing the Options:** - **A. The motion of a pendulum:** - This is a classic example of harmonic motion, which can be accurately described using classical mechanics. The motion of a pendulum can be predicted using equations derived from Newton's laws, such as \( T = 2\pi\sqrt{\frac{L}{g}} \), where \( T \) is the period, \( L \) is the length of the pendulum, and \( g \) is the acceleration due to gravity. - **B. The behavior of a gas in a closed container:** - This is typically described by classical thermodynamics and kinetic theory. The behavior of gases can be explained using the ideal gas law \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature. While quantum mechanics does play a role at very small scales, the macroscopic behavior of gases is well captured by classical physics. - **C. The photoelectric effect:** - This phenomenon occurs when light (or electromagnetic radiation) hits a material and causes the ejection of electrons from that material. Classical physics could not explain why light below a certain frequency, regardless of its intensity, could not eject electrons. However, quantum mechanics, through the concept of photons (quantized packets of light), explains that each photon has a specific energy given by \( E = hf \), where \( h \) is Planck's constant and \( f \) is the frequency of the light. If the energy of the incoming photons is above a certain threshold, electrons are emitted. This was a pivotal experiment that supported the development of quantum theory. - **D. The trajectory of a projectile:** - This is another classic example of motion that can be described using classical mechanics. The trajectory of a projectile can be predicted using equations of motion under the influence of gravity, such as \( y = y_0 + v_0t - \frac{1}{2}gt^2 \), where \( y \) is the vertical position, \( y_0 \) is the initial position, \( v_0 \) is the initial velocity, and \( g \) is the acceleration due to gravity. ### Why Other Options Are Incorrect or Weaker: - **A, B, and D** are all phenomena that can be accurately described using classical physics principles. They do not require the complex and often counterintuitive principles of quantum mechanics for their explanation. In contrast, the photoelectric effect is fundamentally a quantum phenomenon that cannot be explained without invoking quantum mechanics. ### Common Pitfalls: - Students may confuse the applicability of quantum mechanics with classical physics, especially in scenarios involving small particles or high energies. It's crucial to recognize that while quantum mechanics can describe many phenomena, it is not always necessary for macroscopic systems. - Misunderstanding the threshold frequency in the photoelectric effect can lead to confusion about why certain light does not cause electron emission. ### Revision Summary: - Quantum mechanics governs phenomena at atomic and subatomic levels, while classical physics describes macroscopic systems. - The photoelectric effect is a key example of a quantum phenomenon, explaining electron emission due to light. - Classical mechanics effectively describes the motion of pendulums, gas behavior, and projectile trajectories. - Understanding the limitations of classical physics is essential for grasping when quantum mechanics is necessary.