Question

The laser in an audio CD player uses light with a wavelength of \(7.80 \times 10^{2} \mathrm{~nm} .\) Calculate the frequency of this light.

Short answer

The frequency of the light used by the laser in the audio CD player is approximately \(3.846 \times 10^{14} \mathrm{~Hz}\).

Step-by-step solution

Write down the speed of light, wavelength, and frequency relationship formula

The formula that relates the speed of light (c), wavelength (λ), and frequency (υ) is given by the equation: \[c = \lambda \times \nu \] where c = speed of light \( (3.00 \times 10^8 \mathrm{~m/s}) \) λ = wavelength of light ν = frequency of light

Convert the wavelength from nm to m

The wavelength given in the problem is in nm (nanometers). We need to convert this to meters in order to use this formula. Use the following conversion factor: \(1 \mathrm{~m} = 10^9 \mathrm{~nm} \) So, \(7.80 \times 10^2 \mathrm{~nm} = 7.80 \times 10^2 \times 10^{-9} \mathrm{~m} = 7.80 \times 10^{-7} \mathrm{~m} \).

Rearrange the equation to solve for the frequency

We need to find the frequency (ν), so we need to rearrange the speed of light equation to solve for the frequency: \[\nu = \frac{c}{\lambda}\]

Calculate the frequency of the light

Now, we can plug in the given values for the speed of light (c) and the wavelength (λ) to find the frequency: \[\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \mathrm{~m/s}}{7.80 \times 10^{-7} \mathrm{~m}}\] \[\nu = 3.846 \times 10^{14} \mathrm{~Hz}\] The frequency of the light used by the laser in the audio CD player is approximately \(3.846 \times 10^{14} \mathrm{~Hz}\).