Problem 9 - Chemistry: The Central Science

Question

What are the basic SI units for (a) the wavelength of light, (b) the frequency of light, (c) the speed of light?

Step-by-Step Solution

Answer

The basic SI units are (a) for the wavelength of light: meter (m), (b) for the frequency of light: Hertz (Hz) or s^{-1}, and (c) for the speed of light: meters per second (m/s).

Step 1: (SI Unit of Wavelength of Light)

The wavelength of light is the distance between two consecutive crests (or troughs) in a wave and is commonly represented by the symbol \(\lambda\). The SI unit for distance is meters (m). Thus, the basic SI unit for the wavelength of light is the meter (m).

Step 2: (SI Unit of Frequency of Light)

The frequency of light is the number of wave cycles or oscillations that pass a certain point per unit of time. It is commonly represented by the symbol \(f\) or \(\nu\), and is measured in Hertz (Hz). As Hertz (Hz) is equivalent to cycles per second, it can also be expressed as one cycle per second equaling 1 s^{-1}. Thus, the basic SI unit for the frequency of light is Hertz (Hz) or s^{-1}.

Step 3: (SI Unit of Speed of Light)

The speed of light is the speed at which light waves propagate through a medium or vacuum. It is commonly represented by the symbol \(c\), and has a constant value in a vacuum of approximately \(3.00 \times 10^8 m/s\). Since speed is the ratio of distance to time, it is measured in meters per second (m/s). Thus, the basic SI unit for the speed of light is meters per second (m/s).