Question

multiple choice question
yellow light has a wavelength of 6 × 10⁻⁷ m. given that the speed of light is 3 × 10⁸ m/s, what is the frequency of this light?
1.8 × 10² hz
5 × 10⁻¹⁴ hz
5 × 10¹⁴ hz
2 × 10⁻¹⁵ hz

Explanation:

Step1: Recall the formula

The formula relating speed \(v\), wavelength \(\lambda\), and frequency \(f\) is \(v = f\lambda\). We need to solve for \(f\), so \(f=\frac{v}{\lambda}\).

Step2: Substitute the values

Given \(v = 3\times10^{8}\text{ m/s}\) and \(\lambda=6\times 10^{-7}\text{ m}\). Then \(f=\frac{3\times 10^{8}}{6\times 10^{-7}}\).

Step3: Simplify the expression

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{3}{6}\times10^{8-(- 7)}\). \(\frac{3}{6}=0.5\) and \(8-(-7)=15\), so \(f = 0.5\times10^{15}\). In scientific notation \(0.5\times10^{15}=5\times10^{14}\text{ Hz}\).

Answer:

\(5\times 10^{14}\text{ Hz}\) (the third option)