A Level Physics Practice Exam

What is the relationship between energy, frequency, and Planck's constant represented by?

1. E = mv^2

2. E = hf

3. E = hc/wavelength

4. E = 1/2 mv^2

The correct answer is: E = hf

The relationship between energy, frequency, and Planck's constant is expressed by the equation E = hf. In this formula, E represents the energy of a photon, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and f is the frequency of the radiation. This relationship shows that the energy of a photon is directly proportional to its frequency, indicating that higher frequency electromagnetic waves carry more energy. This concept is fundamental in quantum mechanics and explains phenomena such as the photoelectric effect, where light energy can be converted into electrical energy. The connection highlights how light behaves both as a wave and a particle—captured by the notion that the energy of each photon corresponds precisely to its frequency. Other formulas presented involve different physical scenarios. For instance, E = mv^2 is associated with kinetic energy in classical mechanics, and E = 1/2 mv^2 specifically relates to kinetic energy as well but does not incorporate Planck's constant or frequency. The equation E = hc/wavelength connects energy to wavelength but does so indirectly through the speed of light (c) and does not directly emphasize frequency. Thus, E = hf accurately captures the essence of the relationship being asked about.