To understand electromagnetic radiation and be able to perform calculations invo

Question

To understand electromagnetic radiation and be able to perform calculations involving wavelength, frequency, and energy. Several properties are used to define waves. Every wave has a wavelength, which is the distance from peak to peak or trough to trough. Wavelength, typically given the symbol lambda (lowercase Greek "lambda"), is usually measured in meters. Every wave also has a frequency, which is the number of wavelengths that pass a certain point during a given period of time. Frequency, given the symbol nu (lowercase Greek'nu'), is usually measured in inverse seconds (s-1)- Hertz (Hz), another unit of frequency, is equivalent to inverse seconds. The product of wavelength and frequency is the speed in meters per second (m/s). For light waves, the speed is constant. The speed of light is symbolized by the letter c and is always equal to 2.998 x 10s m/s in a vacuum; that is, c=lambda nu = 2.998 times 108 m/s Another term for "light" is electromagnetic radiation, which encompasses not only visible light but also gamma rays, X-rays, UV rays, infrared rays, microwaves, and radio waves. As you could probably guess, these different kinds of radiation are associated with different energy regimes. Gamma rays have the greatest energy, whereas radio waves have the least energy. The energy (measured in joules) of a particular kind of light wave is equal to its frequency times a constant called Planck's constant, symbolized h : E = h nu A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz), where i MHz = 106+ Hz. Calculate the broadcast wavelength of the radio station 105.9 FM. Express your answer to four significant figures and include the appropriate units. Green light has a frequency of about (j.00 x 10H s-1. What is the energy of green light? Express your answer to three significant figures and include the appropriate units. Hospital X-ray generators emit X-rays with wavelength of about 15.0 nanometers (nm), where ] nm = 10-9 m. What is the energy of the X-rays? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A) 105.9 FM = 105.9 x10^6 Hz wavelength = c/f = 3 x10^ 8/(105.9 x10^6) =2.832 meters B) f = 6 x10^ 14 , E = hf = 6.625 x10^ -34 x 6 x10^ 14 = 3.975 x10^ -19 Joules C) wavelenght = 15 nm = 15 x10^ -9 m , f = 3 x10^ 8/15 x10^ -9 = 2 x 10^ 16 E = hf = 6.625 x10^ -34 x 2 x10^ 16 = 1.325 x10^ -17 Joules

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