Question

fill in the blank question
green light has a frequency of 6 × 10¹⁴ hz, and the speed of light is 3 × 10⁸ m/s. the wavelength of green light is × 10⁻⁷.

Explanation:

Step1: Recall the formula

The formula relating speed \(v\), frequency \(f\), and wavelength \(\lambda\) is \(v = f\lambda\). We can rearrange it to find \(\lambda=\frac{v}{f}\).

Step2: Substitute the values

Given \(v = 3\times10^{8}\text{ m/s}\) and \(f = 6\times 10^{14}\text{ Hz}\). Then \(\lambda=\frac{3\times 10^{8}}{6\times 10^{14}}\).
Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{3}{6}\times10^{8-14}\).
\(\frac{3}{6}=0.5\) and \(10^{8 - 14}=10^{-6}\). So \(\lambda = 0.5\times10^{-6}\).
We can rewrite \(0.5\times10^{-6}\) as \(5\times10^{-7}\) (since \(0.5\times10^{-6}=5\times10^{-1}\times10^{-6}=5\times10^{-7}\)).

Answer:

\(5\)