Question

a beam of light has a frequency of ( 6.00\times10^{14} \text{hz} ). using the speed of light (( c = 3.00\times10^{8} \text{m/s} )), which of the following options shows the correct numerical setup to calculate the wavelength of this light?
( lambda=\frac{3.00\times10^{8} \text{m/s}}{6.00\times10^{14}/s}\times\frac{1}{2} )
( lambda=(3.00\times10^{8} \text{m/s})\times(6.00\times10^{14}/s) )
( lambda=\frac{3.00\times10^{8} \text{m/s}}{6.00\times10^{14}/s} )
( lambda=\frac{6.00\times10^{14}/s}{3.00\times10^{8} \text{m/s}} )

Explanation:

Step1: Recall the formula for the speed of light

The speed of light \(c\) is related to frequency \(f\) and wavelength \(\lambda\) by the formula \(c = \lambda f\).

Step2: Solve the formula for wavelength

To find \(\lambda\), we rearrange the formula \(c=\lambda f\) to \(\lambda=\frac{c}{f}\).
Given \(c = 3.00\times 10^{8}\text{ m/s}\) and \(f=6.00\times 10^{14}\text{ /s}\), substituting into the formula gives \(\lambda=\frac{3.00\times 10^{8}\text{ m/s}}{6.00\times 10^{14}\text{ /s}}\)

Answer:

\(\lambda=\frac{3.00\times 10^{8}\text{ m/s}}{6.00\times 10^{14}\text{ /s}}\) (the third option)