violet light has a frequency of 7.26×10¹⁴ hz and travels at a speed of 3.00×10⁸ m/s. 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 $\lambda=\frac{v}{f}$.

Step2: Substitute the given values

Given $v = 3.00\times10^{8}\ m/s$ and $f = 7.26\times 10^{14}\ Hz$, we substitute into the formula: $\lambda=\frac{3.00\times 10^{8}}{7.26\times 10^{14}}\ m$.

Step3: Calculate the wavelength in meters

$\lambda=\frac{3.00}{7.26}\times10^{8 - 14}\ m\approx0.413\times10^{-6}\ m = 413\times10^{-9}\ m$.

Step4: Convert to nanometers

Since $1\ nm=10^{-9}\ m$, the wavelength in nanometers is $\lambda = 413\ nm$.

Answer:

413