Question

what is the wavelength of blue light that has a frequency of 6.47e14 s⁻¹? (c = 3.00×10⁸ m/s)

Explanation:

Step1: Recall the wave - speed formula

The speed of light formula is $c = \lambda
u$, where $c$ is the speed of light, $\lambda$ is the wavelength, and $
u$ is the frequency. We need to solve for $\lambda$, so $\lambda=\frac{c}{
u}$.

Step2: Substitute the given values

Given $c = 3.00\times10^{8}\text{ m/s}$ and $
u=6.47\times 10^{14}\text{ s}^{-1}$. Then $\lambda=\frac{3.00\times 10^{8}\text{ m/s}}{6.47\times 10^{14}\text{ s}^{-1}}$.

Step3: Perform the calculation

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we have $\lambda=\frac{3.00}{6.47}\times10^{8-14}\text{ m}$. $\frac{3.00}{6.47}\approx0.464$, and $10^{8 - 14}=10^{-6}$. So $\lambda\approx4.64\times 10^{-7}\text{ m}$.

Answer:

$4.64\times 10^{-7}\text{ m}$