Which among the following statements is TRUE? Select one: a As the energy increases; the frequency of radiation decreases: b As the wavelength increases, the frequency also increases € The wavelength of light is inversely related to its energy: Red light has a shorter wavelength than violet light
The Correct Answer and Explanation is:
The correct answer is: The wavelength of light is inversely related to its energy.
To understand why, let us explore the fundamental relationships among wavelength, frequency, and energy in the context of electromagnetic radiation. Light behaves both as a wave and a particle. Its energy EE is directly proportional to its frequency ff, expressed by the equation:
E=hfE = hf
where hh is Planck’s constant.
Simultaneously, the frequency and wavelength λ\lambda of light are related by the equation:
c=fλc = f\lambda
where cc is the speed of light in a vacuum. By combining these equations, energy becomes inversely proportional to wavelength:
E=hcλE = \frac{hc}{\lambda}
This means that as the wavelength increases, the energy decreases, and vice versa. Hence, shorter wavelengths carry more energy, and longer wavelengths carry less.
Let us analyze the other options for clarity:
- Option a is incorrect. Since energy and frequency are directly proportional, if energy increases, so does frequency.
- Option b is also false. Frequency and wavelength are inversely related. As one increases, the other decreases.
- Option d is incorrect. Red light has a longer wavelength and lower frequency compared to violet light. Violet light lies at the higher-energy end of the visible spectrum and has the shortest wavelength.
Therefore, the only statement that aligns with the established principles of wave-particle duality in light is that wavelength is inversely related to energy. This inverse relationship is crucial for understanding phenomena such as the photoelectric effect and spectroscopy. It explains why ultraviolet rays are more energetic and potentially harmful than infrared radiation.
