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Consider electromagnetic waves propagating in air. (a) Determine the frequency of a wave with a wavelength of (i) 5.0 km, (ii) 5.0 \mu \mathrm{m}5.0μm, (iii) 5.0 nm. (b) What is the wavelength (in meters and nanometers) of (i) gamma rays of frequency 6.50 \times 10^{21} \mathrm{Hz}6.50×1021Hz and (ii) an AM station radio wave of frequency 590 kHz?
Consider electromagnetic waves propagating in air. (a) Determine the frequency of a wave with a wavelength of (i) 5.0 km, (ii) 5.0 \mu \mathrm{m}5.0μm, (iii) 5.0 nm. (b) What is the wavelength (in meters and nanometers) of (i) gamma rays of frequency 6.50 \times 10^{21} \mathrm{Hz}6.50×1021Hz and (ii) an AM station radio wave of frequency 590 kHz?
(a) (i)Frequency≈ 6.00 × 10^4 Hz (ii) Frequency ≈ 6.00 × 10^13 Hz (iii) Frequency ≈ 6.00 × 10^16 Hz(b) (i)Wavelength≈ 4.62 × 10^-14 m (or 462 nm) (ii) Wavelength ≈ 508.47 m (or 508,470 nm)(a) The frequency of anelectromagnetic wavecan be determined using the formula:frequency = speed of light / wavelength. In air, the speed of light is approximately 3.0 x 10^8 meters per second.(i) For a wavelength of 5.0 km (5.0 x 10^3 meters), the frequency can be calculated as:frequency = (3.0 x 10^8 m/s) / (5.0 x 10^3 m)= 6.0 x 10^4 Hz.(ii) For a wavelength of 5.0 μm (5.0 x 10^-6 meters), the frequency can be calculated as:frequency = (3.0 x 10^8 m/s) / (5.0 x 10^-6 m)= 6.0 x 10^13 Hz.(iii) For a wavelength of 5.0 nm (5.0 x 10^-9 meters), the frequency can be calculated as:frequency = (3.0 x 10^8 m/s) / (5.0 x 10^-9 m)= 6.0 x 10^16 Hz.(b) To determine the wavelength of a wave, we can rearrange the formula as wavelength =speed of light/ frequency.(i) Forgamma rayswith a frequency of 6.50 x 10^21 Hz, the wavelength can be calculated as:wavelength = (3.0 x 10^8 m/s) / (6.50 x 10^21 Hz)≈ 4.62 x 10^-14 meters or 4.62 nm.(ii) For an AM stationradio wavewith a frequency of 590 kHz (590 x 10^3 Hz), the wavelength can be calculated as: wavelength = (3.0 x 10^8 m/s) / (590 x 10^3 Hz)≈ 508 meters or 5.08 x 10^8 nm.Therefore, the frequency and wavelength ofelectromagnetic wavesin air can be determined using the speed of light and the given values of wavelength or frequency.Learn more aboutelectromagnetic waves,herebrainly.com/question/14953576#SPJ11...