yellow light has a frequency of 5.2×10¹⁴ hz and travels at a speed of 3.0×10⁸ m/s. what is the wavelength of…

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. We need to solve for $\lambda$, so we can rewrite the formula as $\lambda=\frac{v}{f}$.

Step2: Substitute the given values

We are given that $v = 3.0\times10^{8}\text{ m/s}$ and $f = 5.2\times10^{14}\text{ Hz}$. Substituting these values into the formula $\lambda=\frac{v}{f}$, we get $\lambda=\frac{3.0\times 10^{8}}{5.2\times 10^{14}}$.

Step3: Perform the calculation

Using the rules of exponents for division ($\frac{a^{m}}{a^{n}}=a^{m - n}$), we have $\lambda=\frac{3.0}{5.2}\times10^{8-14}$. $\frac{3.0}{5.2}\approx0.58$ and $10^{8 - 14}=10^{-6}$. So $\lambda\approx0.58\times10^{-6}=5.8\times10^{-7}\text{ m}$.

Answer:

$5.8\times 10^{-7}\text{ m}$