ily task 10.1: Classwork/Homework/Data-interpretation e the above of the electromagnetic spectrum to answer the following questions. Which type of EM radiation has the: Longest wavelength? Shortest wavelength? Highest energy? Lowest frequency? Give one word for each of the following descriptions. The type of radiation that can travel through flesh, but not through bones. It therefore casts a shadow of bones. The type of radiation that causes the skin to become brown. Visible light with the longest wavelength. Use the wave equation \( v=\mathrm{f} \lambda \) to answer the following questions. Calculate the highest frequency that radio waves can have. Calculate the lowest frequency that gamma rays can have. ( \( 1 \mathrm{~nm}=1 \times 10^{-9} \mathrm{~m} \) ) What is the main difference between radio waves and gamma rays? Radio waves tend to move around objects, while gamma rays tend to move through objects. Give a possible explanation for this phenomenon. What frequencies of light are visible to the human eye? ( \( 1 \mathrm{~nm}=1 \times 10^{-9} \mathrm{~m} \) ) Calculate the highest energy associated with X rays.

To answer your questions about the electromagnetic spectrum, let's break it down step by step. ### EM Radiation Characteristics 1. **Longest wavelength**: Radio waves 2. **Shortest wavelength**: Gamma rays 3. **Highest energy**: Gamma rays 4. **Lowest frequency**: Radio waves ### One-word Descriptions 1. **The type of radiation that can travel through flesh, but not through bones**: X-rays 2. **The type of radiation that causes the skin to become brown**: Ultraviolet (UV) 3. **Visible light with the longest wavelength**: Red ### Wave Equation Calculations The wave equation is given by: \[ v = f \lambda \] where: - \( v \) is the speed of light (\( c \approx 3 \times 10^8 \, \text{m/s} \)) - \( f \) is the frequency - \( \lambda \) is the wavelength #### 1. Calculate the highest frequency that radio waves can have. Radio waves have wavelengths that can be very long, but let's assume a typical maximum wavelength for radio waves is around \( 1 \, \text{m} \) (for example). Using the wave equation: \[ f = \frac{v}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{1 \, \text{m}} = 3 \times 10^8 \, \text{Hz} \] #### 2. Calculate the lowest frequency that gamma rays can have. Gamma rays have very short wavelengths, typically in the range of \( 0.01 \, \text{nm} \) to \( 0.1 \, \text{nm} \). Let's use \( 0.1 \, \text{nm} \) for this calculation. Convert \( 0.1 \, \text{nm} \) to meters: \[ 0.1 \, \text{nm} = 0.1 \times 10^{-9} \, \text{m} = 1 \times 10^{-10} \, \text{m} \] Now, calculate the frequency: \[ f = \frac{v}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{1 \times 10^{-10} \, \text{m}} = 3 \times 10^{18} \, \text{Hz} \] ### Main Difference Between Radio Waves and Gamma Rays **Radio waves tend to move around objects, while gamma rays tend to move through objects.** #### Possible Explanation for This Phenomenon The difference in behavior can be attributed to their wavelengths and energies. Radio waves have much longer wavelengths and lower energy, allowing them to diffract around obstacles. In contrast, gamma rays have very short wavelengths and high energy, which allows them to penetrate materials more effectively. ### Frequencies of Light Visible to the Human Eye The visible spectrum ranges approximately from \( 400 \, \text{nm} \) (violet) to \( 700 \, \text{nm} \) (red). #### Convert to Hz Using the wave equation: - For \( 400 \, \text{nm} \): \[ f = \frac{3 \times 10^8 \, \text{m/s}}{400 \times 10^{-9} \, \text{m}} = 7.5 \times 10^{14} \, \text{Hz} \] - For \( 700 \, \text{nm} \): \[ f = \frac{3 \times 10^8 \, \text{m/s}}{700 \times 10^{-9} \, \text{m}} = 4.29 \times 10^{14} \, \text{Hz} \] ### Calculate the Highest Energy Associated with X-rays The energy of a photon can be calculated using the formula: \[ E = hf \] where: - \( h \) is Planck's constant (\( h \approx 6.626 \times 10^{-34} \, \text{J s} \)) - \( f \) is the frequency Assuming a typical frequency for X-rays is around \( 10^{16} \, \text{Hz} \): \[ E = (6.626 \times 10^{-34} \, \text{J s})(10^{16} \, \text{Hz}) \approx 6.626 \times 10^{-18} \, \text{J} \] This is a rough estimate, as X-ray frequencies can vary widely. ### Summary - Longest wavelength: Radio waves - Shortest wavelength: Gamma rays - Highest energy: Gamma rays - Lowest frequency: Radio waves - X-rays: Type of radiation that can travel through flesh but not bones. - UV: Type of radiation that causes skin to brown. - Red: Visible light with the longest wavelength. - Highest frequency of radio waves: \( 3 \times 10^8 \, \text{Hz} \) - Lowest frequency of gamma rays: \( 3 \times 10^{18} \, \text{Hz} \) - Visible light frequencies: Approximately \( 4.29 \times 10^{14} \, \text{Hz} \) to \( 7.5 \times 10^{14} \, \text{Hz} \) - Highest energy associated with X-rays: Approximately \( 6.626 \times 10^{-18} \, \text{J} \) (depending on frequency used).