The correct option is **A. Infra-red rays**. ### Explanation of the Correct Answer Electromagnetic waves are categorized based on their wavelengths and frequencies, which directly relate to their energy. The energy of electromagnetic radiation can be calculated using the formula: \[ E = h \cdot f \] where: - \(E\) is the energy of the wave, - \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)), - \(f\) is the frequency of the wave. Since frequency and wavelength are inversely related (given by the equation \(c = \lambda \cdot f\), where \(c\) is the speed of light and \(\lambda\) is the wavelength), we can also express energy in terms of wavelength: \[ E = \frac{h \cdot c}{\lambda} \] From this equation, we can see that as the wavelength (\(\lambda\)) increases, the energy (\(E\)) decreases. Therefore, the longer the wavelength, the less energetic the electromagnetic wave. #### Energy Ranking of the Given Options 1. **Gamma rays**: These have the shortest wavelengths (less than \(0.01 \, \text{nm}\)) and the highest frequencies, making them the most energetic electromagnetic waves. 2. **X-rays**: These have slightly longer wavelengths (ranging from \(0.01 \, \text{nm}\) to \(10 \, \text{nm}\)) than gamma rays, thus they are less energetic than gamma rays but still very high in energy. 3. **Ultra-violet rays**: These have wavelengths ranging from about \(10 \, \text{nm}\) to \(400 \, \text{nm}\). They are less energetic than X-rays but more energetic than visible light. 4. **Infra-red rays**: These have longer wavelengths (ranging from about \(700 \, \text{nm}\) to \(1 \, \text{mm}\)), making them the least energetic among the options provided. ### Why the Other Options Are Incorrect - **B. X-rays**: As mentioned, X-rays have shorter wavelengths than infrared rays, which means they have higher energy. Therefore, they cannot be the least energetic. - **C. Ultra-violet rays**: UV rays also have shorter wavelengths than infrared rays, which means they are more energetic. Thus, they are not the least energetic option. - **D. Gamma rays**: Gamma rays are the most energetic electromagnetic waves due to their very short wavelengths. They are far more energetic than infrared rays, making this option incorrect. ### Summary of Key Points - The energy of electromagnetic waves is inversely related to their wavelength; longer wavelengths correspond to lower energy. - Infra-red rays have the longest wavelengths among the options provided, making them the least energetic. - The order of energy from least to most energetic in the given options is: Infra-red rays < Ultra-violet rays < X-rays < Gamma rays. - Understanding the relationship between wavelength, frequency, and energy is crucial for identifying the energy levels of different types of electromagnetic radiation. This understanding will help you in various physics problems related to electromagnetic waves and their properties.