Learning Goal: To understand electromagnetic radiation and be able to perform ca

Question

Learning Goal: 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 A (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 v (lowercase Greek "nu"), is usually measured in inverse seconds (s^minim 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 (in/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 10^8 m/s in a vacuum; that is. c = lambda u = 2.998 x 10^8 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 photon for a particular kind of light wave is equal to its frequency times a constant called Planck's constant, symbolized h : E_photon = h v h = 6.626 x 10^minim 34 J middot s These two equations can be combined to give an equation that relates energy to wavelength: E = hc/lambda A radio station's channel, such as 100.7 FM or 92.3 FM. is actually its frequency in megahertz (MHz), where 1 MHz = 10^6 Hz and 1 Hz = 1 s ^minim 1. Calculate the broadcast wavelength of the radio station 99.30 FM. Express your answer to four significant figures and include the appropriate units.

Explanation / Answer

Data.

1 MHz = 106 Hz = s-1

Speed of light = c = 2.998 x 108 m/s

Planck's constant = h = 6.626 x 10-34 J.s

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Answer.

For this case we need to solve the wavelenght of a 99.30 MHz frecuency.

E = c/

We don't involve planck's constant because we're not analizing this in terms of Energy (Joules), so we can proceed as follows;

= c/E

= (2.998 x 108 m/s)/(99.30 x 106 s-1)

= 3.0191 m

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The wavelength of the 99.30 FM radio frecuency is 3.0191 m.

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