Question

a wave has a frequency of 5.1 × 10^14 hz. what is the wavelength?
5.1 × 10^7 m
5.9 × 10^(-7) m
1.53 × 10^23 m
1.7 × 10^6 m

Explanation:

Step1: Recall wave - speed formula

The speed of light $c = \lambda f$, where $c = 3\times10^{8}\text{ m/s}$ (speed of light in vacuum), $\lambda$ is the wavelength, and $f$ is the frequency. We need to solve for $\lambda$, so $\lambda=\frac{c}{f}$.

Step2: Substitute values

Given $f = 5.1\times 10^{14}\text{ Hz}$ and $c = 3\times 10^{8}\text{ m/s}$. Then $\lambda=\frac{3\times 10^{8}}{5.1\times 10^{14}}$.

Step3: Calculate wavelength

Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\lambda=\frac{3}{5.1}\times10^{8 - 14}\approx0.59\times10^{- 6}=5.9\times10^{-7}\text{ m}$.

Answer:

B. $5.9\times 10^{-7}\text{ m}$