Question

what is the wavelength (in nm) of blue light that has a frequency of 6.35×10¹⁴ s⁻¹? (c = 3.00×10⁸ m/s)

Explanation:

Step1: Recall the formula

The formula relating the speed of light ($c$), frequency ($
u$), and wavelength ($\lambda$) is $c = \lambda
u$. We want to find $\lambda$, so we can rewrite it as $\lambda=\frac{c}{
u}$.

Step2: Substitute the given values

Given $c = 3.00\times 10^{8}\text{ m/s}$, and $
u = 6.35\times 10^{14}\text{ s}^{-1}$. First, we calculate $\lambda$ in meters: $\lambda=\frac{3.00\times 10^{8}\text{ m/s}}{6.35\times 10^{14}\text{ s}^{-1}}=\frac{3.00}{6.35}\times10^{8 - 14}\text{ m}\approx0.472\times 10^{-6}\text{ m}$.

Step3: Convert to nanometers

Since $1\text{ m}=10^{9}\text{ nm}$, then $\lambda = 0.472\times 10^{-6}\text{ m}\times10^{9}\text{ nm/m}=472\text{ nm}$.

Answer:

472