2PE: Calculating Frequency from Wavelength The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation? (a) A laser used in orthopedic spine surgery produces radiation with a wavelength of 2.10 pm. Calculate the frequency of this radiation, (b) An FM radio station broadcasts electromagnetic radiation at a frequency of 103.4 MHz (megahertz; 1 MHz = 106 s-1). Calculate the wavelength of this radiation. The speed of light is 2.998 x 108 m/s to four significant figures.
Solution: Here, we are going to calculate the wavelengths and frequencies of the given radiation. Step1: The distance between two adjacent crests or troughs is called wavelength. It is denoted by the o o -10 greek letter lambda() and is generally expressed in terms of Angstrom units(A ) [1 A = 10 m] On the other hand, the number of waves which pass through a given point in one second is known as the frequency. It is denoted by the greek letter nu() and is generally expressed in -1 terms of Hertz(Hz) [1 Hz = 1 sec ] If c is the velocity of light, the the relation between wavelength, frequency and velocity of light is given by: c = x ------(1) Step2: a) Given, wavelength of the radiation = 2.10 m -6 -6 = 2.10 x 10 m [1 m = 10 m] Therefore, from equation (1), frequency() = c/ 8 -6 Substituting the values, we get, = (2.998 x 10 m/sec) / (2.10 x 10 m) 14 -1 = 1.43 x 10 sec . Thus, frequency of the radiation is 1.43 x 10 sec . 14 -1 Step3: b) Given, frequency of the radiation = 103.4 MHz 8 -1 = 1.034 x 10 sec . Therefore, from equation (1), wavelength() = c/ 8 8 -1 Substituting the values, we get, = (2.998 x 10 m/sec) / (1.034 x 10 sec ) = 2.899 m. Thus, wavelength of the radiation is 2.899 m. ----------------------