》) Activity 2 Test yourself Interpreting the electromagnetic spectrum 1 Here is a mixed-up list of the different types microwaves; visible light; X-rays; infrared ligh ultraviolet light Arrange them in order of a) increasing frequencies b) increasing wavelengths c) increasing energy. 2 Calculate the frequencies of these waves: a) a radio wave with a wavelength of 2 met b) yellow light with a wavelength of 600 nn c) an X-ray with a wavelength of \( 10^{-12} \mathrm{~m} \). 3 Calculate the wavelengths of these: a) a cell phone that sends frequencies of 2, b) ultraviolet light with a frequency of \( 10^{16} \) c) a gamma ray with the frequency of \( 10^{19} \)

Let's break down the problem step by step. ### 1. Arranging the types of electromagnetic waves The electromagnetic spectrum can be arranged based on frequency, wavelength, and energy. The general order from lowest to highest frequency (and thus longest to shortest wavelength and lowest to highest energy) is: - Radio waves - Microwaves - Infrared light - Visible light - Ultraviolet light - X-rays - Gamma rays #### a) Increasing frequencies: - Radio waves - Microwaves - Infrared light - Visible light - Ultraviolet light - X-rays #### b) Increasing wavelengths: - X-rays - Ultraviolet light - Visible light - Infrared light - Microwaves - Radio waves #### c) Increasing energy: - Radio waves - Microwaves - Infrared light - Visible light - Ultraviolet light - X-rays ### 2. Calculating the frequencies of the waves The frequency \( f \) of a wave can be calculated using the formula: \[ f = \frac{c}{\lambda} \] where: - \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)) - \( \lambda \) is the wavelength in meters. #### a) Radio wave with a wavelength of 2 m: \[ f = \frac{3 \times 10^8 \, \text{m/s}}{2 \, \text{m}} = 1.5 \times 10^8 \, \text{Hz} \] #### b) Yellow light with a wavelength of 600 nm (which is \( 600 \times 10^{-9} \, \text{m} \)): \[ f = \frac{3 \times 10^8 \, \text{m/s}}{600 \times 10^{-9} \, \text{m}} = 5 \times 10^{14} \, \text{Hz} \] #### c) X-ray with a wavelength of \( 10^{-12} \, \text{m} \): \[ f = \frac{3 \times 10^8 \, \text{m/s}}{10^{-12} \, \text{m}} = 3 \times 10^{20} \, \text{Hz} \] ### 3. Calculating the wavelengths of the waves The wavelength \( \lambda \) can be calculated using the formula: \[ \lambda = \frac{c}{f} \] #### a) Cell phone that sends frequencies of 2 GHz (which is \( 2 \times 10^9 \, \text{Hz} \)): \[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{2 \times 10^9 \, \text{Hz}} = 0.15 \, \text{m} \] #### b) Ultraviolet light with a frequency of \( 10^{16} \, \text{Hz} \): \[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{10^{16} \, \text{Hz}} = 3 \times 10^{-8} \, \text{m} \] #### c) Gamma ray with a frequency of \( 10^{19} \, \text{Hz} \): \[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{10^{19} \, \text{Hz}} = 3 \times 10^{-11} \, \text{m} \] ### Summary of Results 1. **Order of electromagnetic waves:** - Increasing frequencies: Radio waves, Microwaves, Infrared light, Visible light, Ultraviolet light, X-rays - Increasing wavelengths: X-rays, Ultraviolet light, Visible light, Infrared light, Microwaves, Radio waves - Increasing energy: Radio waves, Microwaves, Infrared light, Visible light, Ultraviolet light, X-rays 2. **Frequencies:** - Radio wave (2 m): \( 1.5 \times 10^8 \, \text{Hz} \) - Yellow light (600 nm): \( 5 \times 10^{14} \, \text{Hz} \) - X-ray (\( 10^{-12} \, \text{m} \)): \( 3 \times 10^{20} \, \text{Hz} \) 3. **Wavelengths:** - Cell phone (2 GHz): \( 0.15 \, \text{m} \) - Ultraviolet light (\( 10^{16} \, \text{Hz} \)): \( 3 \times 10^{-8} \, \text{m} \) - Gamma ray (\( 10^{19} \, \text{Hz} \)): \( 3 \times 10^{-11} \, \text{m} \)