Question

do now 16 (module 4 - lesson 2)
question 1. green light has a frequency of 6.01 x 10¹⁴ hz. what is the wavelength?
○ 1.50 x 10⁻⁷ m
○ 2.00 x 10⁻⁷ m
○ 4.99 x 10⁻⁷ m
○ 6.00 x 10⁻⁷ m

Explanation:

Step1: Recall the formula

The formula relating the speed of light \(c\), frequency \(f\), and wavelength \(\lambda\) is \(c = f\lambda\). The speed of light \(c = 3\times10^{8}\text{ m/s}\).

Step2: Solve for \(\lambda\)

Rearrange the formula to \(\lambda=\frac{c}{f}\). Substitute \(c = 3\times 10^{8}\text{ m/s}\) and \(f=6.01\times 10^{14}\text{ Hz}\) into the formula: \(\lambda=\frac{3\times 10^{8}}{6.01\times 10^{14}}\).
Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\lambda=\frac{3}{6.01}\times10^{8-14}\).
Calculate \(\frac{3}{6.01}\approx0.499\) and \(10^{8 - 14}=10^{-6}\). So \(\lambda\approx4.99\times 10^{-7}\text{ m}\).

Answer:

\(4.99\times 10^{-7}\text{ m}\) (the third option)