1PE: 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? Consider the following three statements: (i) For any electromagnetic radiation, the product of the wavelength and the frequency is a constant, (ii) If a source of light has a wavelength of 3.0 A, its frequency is 1.0 * 1018 Hz. (iii) The speed of ultraviolet light is greater than the speed of microwave radiation. Which of these three statements is or are true? (a) Only one statement is true, (b) Statements (i) and (ii) are true, (c) Statements (i) and (iii) are true, (d) Statements (ii) and (iii) are true, (e) All three statements are true.
Solution: Here, we are going to find which of the given statements are true. Step1: The distance between two adjacent crests or troughs is called wavelength. It is denoted by the greek letter lambda() and is generally expressed in terms of Angstrom units(A ) [1 A = 10 o o -10m] 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: 8 i) As the velocity of light is constant, i.e., 3 x 10 m/sec, so, from equation (1) we can say that the product of wavelength and frequency is constant. Thus, statement (i) is true. ii) From equation (1), we can say that, c = -- Given, wavelength = 3.0 A = 3 x 10 -10m 8 -10 Therefore, frequency() = ( 3 x 10 m/sec) / (3 x 10 m) = 1.0 x 10 sec -1 18 = 1.0 x 10 Hz. Thus, statement (ii) is true. iii) Since, the speed of light is constant for all the radiations, therefore, statement (iii) is false. Hence, the correct option is (b). --------------